In the semi-parametric linear regression model Y=β'X+W with right-censored data, the Buckley-James estimator (BJE) of parameter β is the standard extension of the least squares estimator. Since the original definition of the BJE may not exist, James and Smith (1984) proposed to modify the BJE as a zero-crossing point (ZCP). The definition of the ZCP is clear for $p=1$, but is not clearly defined for p ≥ 2. In this talk, we present our modified definition of the ZCP or the BJE for $p\ge 2$.