This article is concerned with an effective algorithm for the identification of multiple outliers in linear regression. It proposes a hybrid algorithm which employs the least median of squares estimator, instead of the least squares estimator, to construct an Initial clean subset in the stepwise forward search scheme. The performance of the proposed algorithm is evaluated and compared with the existing competitor via an extensive Monte Carlo simulation. The algorithm appears to be superior to the competitor for the most of scenarios explored in the simulation study. Particularly it copes with the masking problem quite well. In addition, the orthogonal decomposition and Its updating techniques are considered to improve the computational efficiency and numerical stability of the algorithm.