XOR based RAID 6 systems outperform other RAID systems. Among the XOR (exclusive OR) based RAID-6 schemes, RDP has better performance than others by a narrow margin. However, the RDP code scheme cannot take full advantage of parallel hardware implementation of XOR codes. In this paper, we propose an extension of the double-erasure-correcting RDP code called EDP, which consists of a parallel decoding scheme. Thus, EDP can improve the decoding velocity of RDP by about 40% without any change to the current RDP configuration for storage.