  We find a new Penrose limit of AdS_5 x 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 x S^5 we also find a new Penrose limit of AdS_4
x CP^3.
