In experimental designs, we encounter sometimes with problems in which the response variable is in linear relation with some other variables. These variables are called covariates. The choice of values of the covariates for a given set-up, attaining minimum variance for estimation of the regression parameters, has attracted attention in recent years. It is seen that the OCDs depend much on the methods of construction of the basic block designs. The model considered as below, Where Y is the vector of observations of order , also , and correspond, respectively, to the vectors of treatment effects, block effects and the covariate effects; and are, respectively, the design matrices of treatment effects and block effects; and Z is the design matrix corresponding to the covariate effects. is a vector of order n with all elements unity. From above model, it is evident that for the estimation of the covariate effects to be orthogonal to the treatment and block effects, the necessary and sufficient conditions are: are necessary and sufficient. Also, when above conditions holds, the regression parameters are estimated with maximum efficiency if and only if, The parameter is estimated most efficiently if Z-matrix satisfies all above conditions. The choice of the Z-matrix is usually difficult under the most general block design set-up But, for binary block designs, it can be easier if each column of the Z-matrix is represented by a matrix W, where the rows of W are corresponded to the treatments and the columns of W are corresponded to the blocks.