1 Go to Manage Prime Membership. 2  Do one of the following: To cancel a paid Amazon Prime membership, click End membership. 3  Note: Paid members who haven't placed an Amazon Prime eligible order are eligible for a full refund.o end your Amazon Prime membership: 1  Go to Manage Prime Membership. 2  Do one of the following: To cancel a paid Amazon Prime membership, click End membership. 3  Note: Paid members who haven't placed an Amazon Prime eligible order are eligible for a full refund.