Let A, $X_1$ and $X_2$ be topological spaces and let $i_1:A\to X_1$, $i_2:A\to X_2$ be continuous maps. For all self-maps $f_A:A\to A$, $f_1:X_1\to X_1$ and $f_2:X_2\to X_2$ such that $f_1{i}_1=i_1{f}_A$ and $f_2{i}_2=i_2{f}_A$ there exists a pushout map f defined on the pushout space $X_1{\bigsqcup }_A{X}_2$. In [F] we proved a formula relating the generalized Lefschetz numbers of f, $f_A$, $f_1$ and $f_2$. We had to assume all the spaces involved were connected because in the original definition of the generalized Lefschetz number given by Husseini in [H] the space was assumed to be connected. So, to extend the result of [F] to the not...