In this study we used triangular partially balanced incomplete block design with twornassociate classes to construct optimal incomplete block designs for complete diallel crossrnsystem IV. A method is proposed to analyze Mating-Environment designs for estimatingrngeneral combining ability and specific combining ability effects of lines. The designsrnderived are all variance-balanced in the sense that the variances of the best linear unbiasedrnestimators of elementary contrasts among general combining ability effects are all thernsame. In this study we report some triangular designs which are found optimal in the sensernof Kempthorne (1956). These designs are not listed by Dey and Midha (1996), Parsad andrnGupta (2004) and Sharma and Fanta (2010). The analysis of these designs is presented withrnhelp of a numerical data