  We give a recursive formula for the Moebius function of an interval
$[\sigma,\pi]$ in the poset of permutations ordered by pattern containment in
the case where $\pi$ is a decomposable permutation, that is, consists of two
blocks where the first one contains all the letters 1, 2, ..., k for some k.
This leads to many special cases of more explicit formulas. It also gives rise
to a computationally efficient formula for the Moebius function in the case
where $\sigma$ and $\pi$ are separable permutations. A permutation is separable
if it can be generated from the permutation 1 by successive sums and skew sums
or, equivalently, if it avoids the patterns 2413 and 3142. A consequence of the
formula is that the Moebius function of such an interval $[\sigma,\pi]$ is
bounded by the number of occurrences of $\sigma$ as a pattern in $\pi$. We also
show that for any separable permutation $\pi$ the Moebius function of $(1,\pi)$
is either 0, 1 or -1.
