Statistical researchers have shown increasing interest in generating conditional multivariate normal distributions. In this paper, we discuss several existing methods for the simulation of multivariate normal distribution truncated on the intersection of a set of hyperplanes. We also propose an approach based on the consideration of an orthonormal basis on the set of constraints. Contrarily to the standard approaches, we do not need to compute the covariance matrix of the posterior distribution and its decomposition. The interest of the proposed approach is shown through numerical examples.