We devise a constraint algorithm that makes the angular velocity of the director of a liquid crystal a constant of motion. When the angular velocity is set equal to zero, a director based coordinate system becomes an inertial frame, This is a great advantage because most thermodynamic properties and time correlation functions of a liquid crystal are best expressed relative to a director based coordinate system. One also prevents the director reorientation from interfering with the tails of the time correlation functions. When the angular velocity is forced to be zero the constraints do not do any work on the system. This makes it possible to prove that ensemble averages of phase functions and time correlation functions are unaffected by the director constraint torques, The constraint algorithm also facilitates generalization of nonequilibrium molecular dynamics algorithms to liquid crystal phases, In order to test the algorithm numerically we have simulated a biaxial nematic phase of a variant of the Gay-Berne fluid [J. G. Gay and B. J. Berne, J. Chem. Phys. 74, 3316 (1981)]. The director constraint algorithm works very well. We have calculated the velocity autocorrelation functions and the self diffusion coefficients. In a biaxial nematic liquid crystal there are three independent components of the self-diffusion tenser. They have been found to be finite and different thus proving that we really simulate a liquid rather than a solid and that the symmetry is biaxial. Simulation of biaxial liquid crystals requires fairly large systems. We have therefore developed an algorithm that we run on a parallel computer instead of an ordinary work station.