  The first-order cosmic ray acceleration at ultrarelativistic shocks is
investigated using the Monte Carlo method. We apply a method of discrete
particle momentum scattering as a model of particle pitch angle diffusion to
reproduce highly anisotropic conditions at the shock wave. Shocks with Lorentz
factors $\gamma$ up to 320 and varying magnetic field inclinations $\psi$ are
considered. Values of diffusion coefficients upstream in the point where energy
spectral indices stabilize to the limit 2.2 were calculated. The obtained
acceleration time does not depend on shock conditions.
