  We describe a hierarchical, highly parallel computer algorithm to perform
searches for unknown sources of continuous gravitational waves -- spinning
neutron stars in the Galaxy -- over wide areas of the sky and wide frequency
bandwidths. We optimize the algorithm for an observing period of 4 months and
an available computing power of 20 Gflops, in a search for neutron stars
resembling millisecond pulsars. We show that, if we restrict the search to the
galactic plane, the method will detect any star whose signal is stronger than
15 times the $1\sigma$ noise level of a detector over that search period. Since
on grounds of confidence the minimum identifiable signal should be about 10
times noise, our algorithm does only 50% worse than this and runs on a computer
with achievable processing speed.
