EVENODD scheme is an efficient parity placement scheme for tolerating double disk failures in RAID (Redundant Arrays of Inexpensive Disks) architectures, and the codes of the EVENODD scheme are also optimal block codes based on exclusive-OR operations which making the complexity of the EVENODD scheme more simpler than other schemes that requires computation over finite fields. In this paper, we presented an alternative decoding algorithm for EVENODD code. Compared with EVENODD, the algorithm can reconstruct straightforwardly up to two faulty disks without increasing the computational complexity of the code. Moreover, some steps of the decoding procedure can be processed in parallel, with equivalent hardware to the encoding, without additional hardware. It can recover rapidly from any two disk failures.