Abstract: In the present study, the solution to the d'Alembert type functional equation f(xy)+f(xy -1 )=f(x)g(y)+h(y) is extended to the study of a system of d'Alembert functional equtions on a group under the condition that the former satisfies f(xyz)=f(xzy) .For this purpose, a new function is introduced and the system of functional equations on a group is decomposed into independent equations. A new symbol is used to show the general solution to a system of functional equations on a group.

Key words: system of functional equations, general solution, group, d'Alembert type