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In the present paper it is shown that if $S_1$ and $S_2$ are two
Clifford topological semigroups satisfying certain conditions and
$T$ is an isometric isomorphism of $LUC(S_1)$ onto $LUC(S_2)$,
then $T$ maps $S_1$ topologically isomorphically onto $S_2$.
Furthermore, $T$ maps $M^{l}_{n}(S_1) (M(S_1)$, respectively)
isometrically isomorphically onto $M^{l}_{n}(S_2) (M(S_2)$,
respectively). Indeed, we have obtained a generalization of a
well-known result of Ghahramani, Lau and Losert for locally
compact groups to a more general setting of Clifford topological
semigroups.
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