We give the general form of the vertex corresponding to the interactio
n of an arbitrary number of strings. The technique employed relies on
the ''comma'' representation of string field theory where string field
s and interactions are represented as matrices and operations between
them such as multiplication and trace. The general formulation present
ed here shows that the interaction vertex of N strings, for any arbitr
ary N, is given as a function of particular combinations of matrices c
orresponding to the change of representation between the full string a
nd the half string degrees of freedom.