Because of high cost of each experiment, experimenters like to estimate all the main effects by using minimal number of design points. Many constructive algorithms for finding optimal or near-optimal designs have been developed. A well known and powerful tool to find A-optimal design is Mitchell's algorithm with slight modification. However, if inclusion of more experiments is permitted, we shall be interested in seeking a first-order model with two-factor interactions. In this paper, we apply a partition technique to the linear regression model with some two-factor interactions. This method successfully transforms a two-factor interactions model into a main effects model.