  As a generalization of a previous work [Phys. Rev. D. {\bf 59}, 105014
(1999)], we compute analytically a class of three-loop vacuum diagrams with two
{\em arbitrarily} different mass scales. We use a decomposition algorithm in
which the integrand of the final integral for the third momentum vector, say,
$k$, becomes independent of the angles of $k$-vector in spherical polar
coordinates. This algorithm proves to be very efficient in obtaining
exclusively all $\e$-pole terms of the given diagram.
