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LOANS RECEIVABLE, NET AND RELATED ALLOWANCE FOR LOAN LOSSES (Schedule of Impaired Loans by Class) (Details) (USD $) In Thousands, unless otherwise specified	Mar. 31, 2015	Sep. 30, 2014
Financing Receivable, Impaired [Line Items]
Recorded Investment With Specific Allowance	$ 1,610us-gaap_ImpairedFinancingReceivableWithRelatedAllowanceRecordedInvestment	$ 2,186us-gaap_ImpairedFinancingReceivableWithRelatedAllowanceRecordedInvestment
Related Allowance	120us-gaap_ImpairedFinancingReceivableRelatedAllowance	385us-gaap_ImpairedFinancingReceivableRelatedAllowance
Recorded Investment With No Specific Allowance	14,008us-gaap_ImpairedFinancingReceivableWithNoRelatedAllowanceRecordedInvestment	15,032us-gaap_ImpairedFinancingReceivableWithNoRelatedAllowanceRecordedInvestment
Total Recorded Investment	15,618us-gaap_ImpairedFinancingReceivableRecordedInvestment	17,218us-gaap_ImpairedFinancingReceivableRecordedInvestment
Total Unpaid Contractual Principal Balance	18,228us-gaap_ImpairedFinancingReceivableUnpaidPrincipalBalance	22,315us-gaap_ImpairedFinancingReceivableUnpaidPrincipalBalance
One-to four-family residential [Member]
Financing Receivable, Impaired [Line Items]
Recorded Investment With Specific Allowance		1,733us-gaap_ImpairedFinancingReceivableWithRelatedAllowanceRecordedInvestment / us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis = mgyr_Residential1To4FamilyRealEstateMember
Related Allowance		42us-gaap_ImpairedFinancingReceivableRelatedAllowance / us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis = mgyr_Residential1To4FamilyRealEstateMember
Recorded Investment With No Specific Allowance	5,795us-gaap_ImpairedFinancingReceivableWithNoRelatedAllowanceRecordedInvestment / us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis = mgyr_Residential1To4FamilyRealEstateMember	6,990us-gaap_ImpairedFinancingReceivableWithNoRelatedAllowanceRecordedInvestment / us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis = mgyr_Residential1To4FamilyRealEstateMember
Total Recorded Investment	5,795us-gaap_ImpairedFinancingReceivableRecordedInvestment / us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis = mgyr_Residential1To4FamilyRealEstateMember	8,723us-gaap_ImpairedFinancingReceivableRecordedInvestment / us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis = mgyr_Residential1To4FamilyRealEstateMember
Total Unpaid Contractual Principal Balance	6,310us-gaap_ImpairedFinancingReceivableUnpaidPrincipalBalance / us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis = mgyr_Residential1To4FamilyRealEstateMember	10,830us-gaap_ImpairedFinancingReceivableUnpaidPrincipalBalance / us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis = mgyr_Residential1To4FamilyRealEstateMember
Commercial real estate
Financing Receivable, Impaired [Line Items]
Recorded Investment With Specific Allowance
Related Allowance
Recorded Investment With No Specific Allowance	5,517us-gaap_ImpairedFinancingReceivableWithNoRelatedAllowanceRecordedInvestment / us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis = us-gaap_CommercialRealEstateMember	5,046us-gaap_ImpairedFinancingReceivableWithNoRelatedAllowanceRecordedInvestment / us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis = us-gaap_CommercialRealEstateMember
Total Recorded Investment	5,517us-gaap_ImpairedFinancingReceivableRecordedInvestment / us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis = us-gaap_CommercialRealEstateMember	5,046us-gaap_ImpairedFinancingReceivableRecordedInvestment / us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis = us-gaap_CommercialRealEstateMember
Total Unpaid Contractual Principal Balance	6,549us-gaap_ImpairedFinancingReceivableUnpaidPrincipalBalance / us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis = us-gaap_CommercialRealEstateMember	6,205us-gaap_ImpairedFinancingReceivableUnpaidPrincipalBalance / us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis = us-gaap_CommercialRealEstateMember
Construction
Financing Receivable, Impaired [Line Items]
Recorded Investment With Specific Allowance		442us-gaap_ImpairedFinancingReceivableWithRelatedAllowanceRecordedInvestment / us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis = us-gaap_ConstructionLoansMember
Related Allowance		332us-gaap_ImpairedFinancingReceivableRelatedAllowance / us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis = us-gaap_ConstructionLoansMember
Recorded Investment With No Specific Allowance	1,701us-gaap_ImpairedFinancingReceivableWithNoRelatedAllowanceRecordedInvestment / us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis = us-gaap_ConstructionLoansMember	1,836us-gaap_ImpairedFinancingReceivableWithNoRelatedAllowanceRecordedInvestment / us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis = us-gaap_ConstructionLoansMember
Total Recorded Investment	1,701us-gaap_ImpairedFinancingReceivableRecordedInvestment / us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis = us-gaap_ConstructionLoansMember	2,278us-gaap_ImpairedFinancingReceivableRecordedInvestment / us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis = us-gaap_ConstructionLoansMember
Total Unpaid Contractual Principal Balance	2,477us-gaap_ImpairedFinancingReceivableUnpaidPrincipalBalance / us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis = us-gaap_ConstructionLoansMember	3,160us-gaap_ImpairedFinancingReceivableUnpaidPrincipalBalance / us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis = us-gaap_ConstructionLoansMember
Home equity lines of credit
Financing Receivable, Impaired [Line Items]
Recorded Investment With Specific Allowance
Related Allowance
Recorded Investment With No Specific Allowance	838us-gaap_ImpairedFinancingReceivableWithNoRelatedAllowanceRecordedInvestment / us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis = us-gaap_HomeEquityMember	829us-gaap_ImpairedFinancingReceivableWithNoRelatedAllowanceRecordedInvestment / us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis = us-gaap_HomeEquityMember
Total Recorded Investment	838us-gaap_ImpairedFinancingReceivableRecordedInvestment / us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis = us-gaap_HomeEquityMember	829us-gaap_ImpairedFinancingReceivableRecordedInvestment / us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis = us-gaap_HomeEquityMember
Total Unpaid Contractual Principal Balance	1,125us-gaap_ImpairedFinancingReceivableUnpaidPrincipalBalance / us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis = us-gaap_HomeEquityMember	987us-gaap_ImpairedFinancingReceivableUnpaidPrincipalBalance / us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis = us-gaap_HomeEquityMember
Commercial business
Financing Receivable, Impaired [Line Items]
Recorded Investment With Specific Allowance	1,610us-gaap_ImpairedFinancingReceivableWithRelatedAllowanceRecordedInvestment / us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis = us-gaap_CommercialLoanMember	11us-gaap_ImpairedFinancingReceivableWithRelatedAllowanceRecordedInvestment / us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis = us-gaap_CommercialLoanMember
Related Allowance	120us-gaap_ImpairedFinancingReceivableRelatedAllowance / us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis = us-gaap_CommercialLoanMember	11us-gaap_ImpairedFinancingReceivableRelatedAllowance / us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis = us-gaap_CommercialLoanMember
Recorded Investment With No Specific Allowance	157us-gaap_ImpairedFinancingReceivableWithNoRelatedAllowanceRecordedInvestment / us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis = us-gaap_CommercialLoanMember	331us-gaap_ImpairedFinancingReceivableWithNoRelatedAllowanceRecordedInvestment / us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis = us-gaap_CommercialLoanMember
Total Recorded Investment	1,767us-gaap_ImpairedFinancingReceivableRecordedInvestment / us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis = us-gaap_CommercialLoanMember	342us-gaap_ImpairedFinancingReceivableRecordedInvestment / us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis = us-gaap_CommercialLoanMember
Total Unpaid Contractual Principal Balance	$ 1,767us-gaap_ImpairedFinancingReceivableUnpaidPrincipalBalance / us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis = us-gaap_CommercialLoanMember	$ 1,133us-gaap_ImpairedFinancingReceivableUnpaidPrincipalBalance / us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis = us-gaap_CommercialLoanMember

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