The problem considered is that of finding D-optimal design for the estimation of covariate parameters and the treatment and block contrasts in a block design set up in the presence of non stochastic controllable covariates, when N=2(mod4), N being the total number of observations. It is clear that when N0 (mod4), it is not possible to find designs attaining minimum variance for the estimated covariate parameters. Conditions for D-optimum designs for the estimation of covariate parameters were established when each of the covariates belongs to the interval [-1, 1]. Some constructions of D-optimal design have been provided for symmetric balanced incomplete block design (SBIBD) with parameters b=v, r=k=v-1, =v-2 when k=2 (mod4) and b is an odd integer. Copyright © Taylor & Francis Group, LLC.