In animal breeding programmes knowledge of the genetic properties of the traits under consideration is the first prerequisite in establishing a selection criterion. Several methods such as ANOVA, ML and REML have been utilised to estimate variance and covariance components in animal breeding data which are usually originate from selection experiments. Modified ML procedure which is so-called restricted maximum likelihood (REML) has been widely used due to its statistical desirable properties. To apply the REML method, a number of algorithms such as DF-REML, EM-REML and scoring have been developed to maximise likelihood function in order to estimate variance and covariance components. Expectation-maximisation (EM-REML) is an algorithm in which first derivatives of the likelihood needs to be evaluated numerically or analytically. The main objective of the present study was to estimate phenotypic and genetic associations among milk, fat and protein yields as well as fat and protein percentages in Iranian Holstein heifers based upon applying the EM-REML method through using a multiple trait animal model.