  We present a two term formula for the M\"obius function of intervals in the
poset of all permutations, ordered by pattern containment. The first term in
this formula is the number of so called normal occurrences of one permutation
in another. Our definition of normal occurrences is similar to those that have
appeared in several variations in the literature on the M\"obius function of
this and other posets, but simpler than most of them. The second term in the
formula is complicated, but we conjecture that it equals zero for a significant
proportion of intervals. We present some cases where the second term vanishes
and others where it is nonzero. Computing the M\"obius function recursively
from its definition has exponential complexity, whereas the computation of the
first term in our formula is polynomial and the exponential part is isolated to
the second term, which seems to often vanish. We also present a result on the
M\"obius function of posets connected by a poset fibration.
