  In this paper $Aut(\Sigma X\vee \Sigma Y)^\#$ the order of the group of
self-homotopy equivalence of wedge spaces is studied. Under the condition of
reducibility, we decompose $ Aut(\bigvee\limits_{t=1}^{k}X_{t})$ to the product
of subgroups which generalizes the known results for $k=2$. Then we also give
the formula for $ Aut(\bigvee\limits_{t=1}^{k}\Sigma X_{t})^{\#}$.

Algebraic Topology