Simply put $PSU(N,N| \mathcal{N} )=U(N,N)\times U(\mathcal{N})/U(1)$. More generally a superalgbera of the form $SU(A|B)$ has a bosonic sub-super-algebra $SU(A) \times SU(B) \times U(1)$. 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 $\mathcal{N}=4$ theory is the $PSU(2,2|4)$. I think a good reference is Beisert's review and various stringy textbooks like Polchinski, BBS, etc.