LOANS RECEIVABLE, NET (Schedule of ALL by Loan Category) (Details) - USD ($) $ in Thousands	Sep. 30, 2016	Sep. 30, 2015
Allowance for Loan Losses:
Balance - Allowance for loans losses	$ 3,056	$ 2,886
Individually evaluated for impairment	39	201
Collectively evaluated for impairment	3,017	2,685
Balance - Loans receivable	457,871	423,290
Loan balance individually evaluated for impairment	9,253	10,637
Loan balance collectively evaluated for impairment	448,618	412,653
Unallocated [Member]
Allowance for Loan Losses:
Balance - Allowance for loans losses	22	79
Individually evaluated for impairment
Collectively evaluated for impairment	22	79
Balance - Loans receivable
Loan balance individually evaluated for impairment
Other [Member]
Allowance for Loan Losses:
Balance - Allowance for loans losses	9	6
Individually evaluated for impairment
Collectively evaluated for impairment	9	6
Balance - Loans receivable	9,355	10,305
Loan balance individually evaluated for impairment
Loan balance collectively evaluated for impairment	9,355	10,305
Commercial business [Member]
Allowance for Loan Losses:
Balance - Allowance for loans losses	976	969
Individually evaluated for impairment	39	201
Collectively evaluated for impairment	937	768
Balance - Loans receivable	38,865	41,485
Loan balance individually evaluated for impairment	1,247	1,756
Loan balance collectively evaluated for impairment	37,618	39,729
Construction [Member]
Allowance for Loan Losses:
Balance - Allowance for loans losses	361	453
Individually evaluated for impairment
Collectively evaluated for impairment	361	453
Balance - Loans receivable	14,939	6,679
Loan balance individually evaluated for impairment
Loan balance collectively evaluated for impairment	14,939	6,679
One-to four-family residential [Member]
Allowance for Loan Losses:
Balance - Allowance for loans losses	542	395
Individually evaluated for impairment
Collectively evaluated for impairment	542	395
Balance - Loans receivable	173,235	169,781
Loan balance individually evaluated for impairment	4,010	3,017
Loan balance collectively evaluated for impairment	169,225	166,764
Commercial real estate [Member]
Allowance for Loan Losses:
Balance - Allowance for loans losses	1,075	931
Individually evaluated for impairment
Collectively evaluated for impairment	1,075	931
Balance - Loans receivable	199,510	173,864
Loan balance individually evaluated for impairment	3,843	5,447
Loan balance collectively evaluated for impairment	195,667	168,417
Home equity lines of credit [Member]
Allowance for Loan Losses:
Balance - Allowance for loans losses	71	53
Individually evaluated for impairment
Collectively evaluated for impairment	71	53
Balance - Loans receivable	21,967	21,176
Loan balance individually evaluated for impairment	153	417
Loan balance collectively evaluated for impairment	$ 21,814	$ 20,759

No definition available.

Name:	us-gaap_FinancingReceivableAllowanceForCreditLossAdditionalInformationAbstract
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

The valuation allowance for financing receivables that are expected to be uncollectible that were collectively evaluated for impairment.

+ References

+ Details

Name:	us-gaap_FinancingReceivableAllowanceForCreditLossesCollectivelyEvaluatedForImpairment
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Amount of valuation allowance for financing receivables that are expected to be uncollectible that were individually evaluated for impairment.

+ References

+ Details

Name:	us-gaap_FinancingReceivableAllowanceForCreditLossesIndividuallyEvaluatedForImpairment1
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

The balance of financing receivables that were collectively evaluated for impairment.

+ References

+ Details

Name:	us-gaap_FinancingReceivableCollectivelyEvaluatedForImpairment
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

The balance of financing receivables that were individually evaluated for impairment.

+ References

+ Details

Name:	us-gaap_FinancingReceivableIndividuallyEvaluatedForImpairment
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Amount of allowance to cover probable credit losses on loans and leases. Includes carryover of or adjustments to the allowance for loan losses in connection with business combinations. Excludes allowance for loans and leases covered under loss sharing agreements.

+ References

Reference 1: http://www.xbrl.org/2003/role/presentationRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 310
-SubTopic 10
-Section 50
-Paragraph 11B
-Subparagraph (g)
-URI http://asc.fasb.org/extlink&oid=66008989&loc=SL6953423-111524

Reference 2: http://www.xbrl.org/2003/role/presentationRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 310
-SubTopic 10
-Section 50
-Paragraph 11B
-Subparagraph (c)(1)
-URI http://asc.fasb.org/extlink&oid=66008989&loc=SL6953423-111524

Reference 3: http://www.xbrl.org/2003/role/presentationRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 942
-SubTopic 210
-Section S99
-Paragraph 1
-Subparagraph (SX 210.9-03.7(d))
-URI http://asc.fasb.org/extlink&oid=6876686&loc=d3e534808-122878

Reference 4: http://www.xbrl.org/2003/role/presentationRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 310
-SubTopic 10
-Section S99
-Paragraph 4
-Subparagraph (SAB Topic 6.L.1)
-URI http://asc.fasb.org/extlink&oid=27010918&loc=d3e74567-122707

Reference 5: http://www.xbrl.org/2003/role/presentationRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 310
-SubTopic 30
-Section 50
-Paragraph 2
-Subparagraph (b)(1)(ii)
-URI http://asc.fasb.org/extlink&oid=6379141&loc=d3e15032-111544

+ Details

Name:	us-gaap_LoansAndLeasesReceivableAllowance
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Amount before allowance of loans and leases held in portfolio, including but not limited to, commercial and consumer loans. Includes deferred interest and fees, undisbursed portion of loan balance, unamortized costs and premiums and discounts from face amounts. Excludes loans and leases covered under loss sharing agreements.

+ References

Reference 1: http://www.xbrl.org/2003/role/presentationRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 310
-SubTopic 10
-Section 45
-Paragraph 2
-URI http://asc.fasb.org/extlink&oid=65884687&loc=d3e4428-111522

+ Details

Name:	us-gaap_LoansAndLeasesReceivableGrossCarryingAmount
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Details

Name:	us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis=us-gaap_UnallocatedFinancingReceivablesMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis=mgyr_FinancingReceivableOtherMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis=us-gaap_CommercialLoanMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis=us-gaap_ConstructionLoansMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis=mgyr_Residential1To4FamilyRealEstateMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis=us-gaap_CommercialRealEstateMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis=us-gaap_HomeEquityMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: