  Menon's identity is a classical identity involving gcd sums and the Euler
totient function $\phi$. We derived the Menon-type identity
$\sum\limits_{\substack{m=1\\(m.n^s)_s=1}}^{n^s}
(m-1,n^s)_s=\Phi_s(n^s)\tau_s(n^s)$ in Czechoslovak Math. J., 72(1):165-176
(2022) where $\Phi_s$ denotes the Klee's function and $(a,b)_s$ denotes a a
generalization of the gcd function. Here we give an alternate method to derive
this identity using the concept of Cohen-Ramanujan sum.
