Under the semi-parametric linear regression model with right-censored data, the Buckley-James estimator (BJE) of the parameter was proposed in (1979) and is the standard extension of the least squares estimator. Buckley and James proposed an iterative algorithm and is currently implemented in R package. But their algorithm often does not lead to an estimate even though the BJE exists. Yu and Wong (2002) proposed a non-iterative algorithm and it can find all possible BJEs. That algorithm is improved in this paper.