  The Laser Interferometer Gravitational-wave Observatory (LIGO) has performed
the fourth science run, S4, with significantly improved interferometer
sensitivities with respect to previous runs. Using data acquired during this
science run, we place a limit on the amplitude of a stochastic background of
gravitational waves. For a frequency independent spectrum, the new limit is
$\Omega_{\rm GW} < 6.5 \times 10^{-5}$. This is currently the most sensitive
result in the frequency range 51-150 Hz, with a factor of 13 improvement over
the previous LIGO result. We discuss complementarity of the new result with
other constraints on a stochastic background of gravitational waves, and we
investigate implications of the new result for different models of this
background.
