1. Incapable of being improved or corrected; hopeless: Jane's mother loved old dolls and the whole house was full of them which made the situation quite irredeemable when they wanted to eat dinner at the dining table, which was also cluttered with old dolls!
2. Referring to currencies which are not convertible at the discretion of the holder: At the little town bank, Jill wanted to exchange her US bills into Euros, but the clerk said it was irredeemable or impossible and she would have to go to another bigger bank for the transaction.