This paper introduces a new algorithm for generating the design matrix X, of a linear regression model, with prespecified simple correlation coefficients between each pair of its columns. Controlling the correlation coefficients among the regressors makes the proposed algorithm useful for simulation studies of biased estimation techniques under linear regression models where different degrees of multicollinearity have to be investigated to judge their performance. Unlike the existing algorithms, the new generated matrices have certain desirable features that will be discussed in the sequel. A small simulation study, reveals some differences between the results obtained from applying the new and the McDonald and Galarneau (1975) algorithms. Our main claim is that, the results associated with the new algorithm describe the true state of nature more precisely.