In this paper some conditions are given for the solution of uniqueness problem for the functional equation $f [F(x,y)] = H [f(x),f(y);x,y]$ when $x,y$ belong to a metric space $E$. If $f_{1}$ and $f_{2}$ are identical on some $E$-neighbourhood $U$ of a point $a \in E$, they are shown to be identical on the entire domain $E$. Further conditions are given for the solution of the uniqueness problem.