Two methods of construction of designs for two-way elimination of heterogeneity are given. The first method is based on the derived and residual designs of symmetrical balanced incomplete block designs. The second method utilises the balanced incomplete block design with parametersv= 2k, b= 2(2k− 1),r= 2k− 1 and λ =k− 1. It is further shown that the designs so constructed are either balanced or partially balanced.