We find a new Penrose limit of AdS ₅ × S ⁵ giving the maximally supersymmetric pp-wave background with two explicit space-like isometries. This is an important missing piece in studying the AdS/CFT correspondence in certain subsectors. In particular whereas the Penrose limit giving one space-like isometry is useful for the SU(2) sector of N = 4 SYM, this new Penrose limit is instead useful for studying the SU(2|3) and SU(1, 2|3) sectors. In addition to the new Penrose limit of AdS ₅ × S ⁵ we also find a new Penrose limit of AdS4 × ℂP ³.