SHARE-BASED COMPENSATION AND WARRANTS - Weighted average assumptions (Details) - Employee stock options - $ / shares	12 Months Ended
Jun. 30, 2021	Jun. 30, 2020
Time-Based
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Market price of common stock on grant date	$ 12.41	$ 10.23
Expected volatility	118.00%	118.00%
Risk free interest rate	0.90%	1.90%
Warrants issued (years)	5 years 8 months 12 days	5 years 8 months 12 days
Dividend yield	0.00%	0.00%
Hybrid
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Market price of common stock on grant date		$ 10.61
Expected volatility		118.00%
Risk free interest rate		2.00%
Warrants issued (years)		8 years
Dividend yield		0.00%

The estimated dividend rate (a percentage of the share price) to be paid (expected dividends) to holders of the underlying shares over the option's term.

Name:	us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedDividendRate
Namespace Prefix:	us-gaap_
Data Type:	num:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

The estimated measure of the percentage by which a share price is expected to fluctuate during a period. Volatility also may be defined as a probability-weighted measure of the dispersion of returns about the mean. The volatility of a share price is the standard deviation of the continuously compounded rates of return on the share over a specified period. That is the same as the standard deviation of the differences in the natural logarithms of the stock prices plus dividends, if any, over the period.

+ References

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedVolatilityRate
Namespace Prefix:	us-gaap_
Data Type:	num:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

The risk-free interest rate assumption that is used in valuing an option on its own shares.

+ References

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsRiskFreeInterestRate
Namespace Prefix:	us-gaap_
Data Type:	num:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.

+ References

No definition available.

+ Details

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

- Definition

Expected term of award under share-based payment arrangement, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents reported fact of one year, five months, and thirteen days.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 718
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (f)(2)(i)
-URI http://asc.fasb.org/extlink&oid=120381028&loc=d3e5070-113901

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 718
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SAB Topic 14.D.2)
-URI http://asc.fasb.org/extlink&oid=115993241&loc=d3e301413-122809

+ Details

Name:	us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardFairValueAssumptionsExpectedTerm1
Namespace Prefix:	us-gaap_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	duration

- Definition

Weighted average grant-date fair value of non-vested options outstanding.

+ References

No definition available.

+ Details

Name:	us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsNonvestedWeightedAverageGrantDateFairValue
Namespace Prefix:	us-gaap_
Data Type:	num:perShareItemType
Balance Type:	na
Period Type:	instant

- Details

Name:	us-gaap_OptionIndexedToIssuersEquityTypeAxis=us-gaap_EmployeeStockOptionMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_AwardTypeAxis=rzlt_StockOptionVestingTimeBasedMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_AwardTypeAxis=rzlt_StockOptionVestingHybridMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: