  The direct detection of gravitational waves is a major goal of current
astrophysics. We provide details of a new method for detecting a stochastic
background of gravitational waves using pulsar timing data. Our results show
that regular timing observations of 40 pulsars each with a timing accuracy of
100 nano-seconds will be able to make a direct detection of the predicted
stochastic background from coalescing black holes within five years. With an
improved pre-whitening algorithm, or if the background is at the upper end of
the predicted range, a significant detection should be possible with only 20
pulsars.
