In the case of noninbred and unselected populations with linkage equilibrium, the additive and dominance genetic effects are uncorrelated and the variance-covariance matrix of the second component is simply a product of its variance by a matrix that can be computed from the numerator relationship matrix A. The aim of this study is to present a new approach to estimate the dominance part with a reduced set of equations and hence a lower computing cost. The method proposed is based on the processing of the residual terms resulting from the BLUP methodology applied to an additive animal model. Best linear unbiased prediction of the dominance component 'delta' is almost identical to the one given by the full mixed model equations. Based on this approach, an algorithm for restricted maximum likelihood (REML) estimation of the variance components is also presented. By way of illustration, two numerical examples are given and a comparison between the parameters estimated with the expectation maximization (EM) algorithm and those obtained by the proposed algorithm is made. The proposed algorithm is iterative and yields estimates that are close to those obtained by EM, which is also iterative.