Simply put PSU(N,N|N)=U(N,N)×U(N)/U(1). More generally a superalgbera of the form SU(A|B) has a bosonic sub-super-algebra SU(A)×SU(B)×U(1). The U(1) phase decouples from the rest of the subalgebra for the case of A=B, e.g. and this is denoted by putting the P letter in front of SU(2,2|4) by which we denote the projective group. Thus, the correct way to say what the full global superalgebra of the N=4 theory is the PSU(2,2|4). I think a good reference is Beisert's review and various stringy textbooks like Polchinski, BBS, etc.