This work introduces a decoding strategy for binary self-dual codes possessing an automorphism of a specific type. The proposed algorithm is a hard decision iterative decoding scheme. The enclosed experiments show that the new decoding concept performs error correction beyond the upper bound for the code correction capability. Moreover, we prove that the requirements for the new algorithm hold for any binary self-dual code having an automorphism of the specific type, which makes decoding of this large group of codes possible.