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A recurring payment can only be deleted if no payments have been created for the schedule and the StartDate is set to today or in the future.

When retrieved calling Get Recurring Payment, deleted recurring payments will still return, however the http response code will be "203 - Non-Authoritative Information". Example:

{
	"Meta": {
		"Errors": null,
		"HttpStatus": "NonAuthoritativeInformation",
		"HttpStatusCode": 203,
		"PagingDetails": null
	},
	"Response": {
		"CustomerId": 8053900,
		"CustomerFirstName": "John",
		"CustomerLastName": "Doe",
		"CustomerCompany": "Great Plumbing",
		"NextScheduleDate": "2018-08-01T06:00:00Z",
		"PauseUntilDate": null,
		"FirstPaymentDone": false,
		"DateOfLastPaymentMade": null,
		"TotalAmountPaid": 0,
		"NumberOfPaymentsMade": 0,
		"EndDate": null,
		"PaymentAmount": 12,
		"PaymentSubType": "Moto",
		"AccountId": 7321631,
		"InvoiceNumber": null,
		"OrderId": null,
		"FirstPaymentAmount": 0,
		"FirstPaymentDate": null,
		"StartDate": "2018-07-04T16:49:18.309Z",
		"ScheduleStatus": "Active",
		"ExecutionFrequencyType": "FirstofMonth",
		"ExecutionFrequencyParameter": 1,
		"Description": null,
		"Id": 1433611,
		"LastModified": "2018-06-27T16:49:19.0526906Z",
		"CreatedOn": "2018-06-27T16:49:19.0526906Z"
	}
}