We present in this article a fast approximate
method for computing the statistics
of number of non self-overlapping matches of motifs
in a random text in the non-uniform Bernoulli model.
This method is well suited for protein motifs where the probability of
self-overlap of motifs is small.
For 96% of the *Prosite* motifs,
the expectations of occurrences of the motifs
in a 7 million amino-acids random database
are computed by the approximate method
with less than 1% error when
compared with the exact method.
Processing of the whole *Prosite* takes
about 30 seconds with the approximate method.
We apply this new method to a comparison of the *C. elegans* and
*S. cerevisiae* proteoms.