Abstract: This paper develops a generalized least squares (GLS) estimator in a linear regression model with serially correlated errors. In particular, the asymptotic optimality of the proposed estimator is established. To obtain this result, we use the modified Cholesky decomposition to estimate the inverse of the error covariance matrix based on the ordinary least squares (OLS) residuals. The resulting matrix estimator maintains positive definite ness and converges to the corresponding population matrix at a suitable rate. The outstanding finite sample performance of the proposed GLS estimator is illustrated using simulation studies and two real datasets.