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This paper deals with the standard multiple linear regression model , where the model matrix X is assumed to be of full column rank. We introduce a new biased estimator for β and discuss its properties in some detail. In particular, we show that our new estimator is superior, in the scalar mean-squared error sense, to both the usual restricted least-squares estimator and to the new biased estimator introduced by Liu (1993). We illustrate our findings with a numerical example based on the widely-analysed dataset on Portland cement, cf. Woods, Steinour and Starke (1932), Hald (1952, pp. 635-652), Piepel and Redgate (1998).