In the linear model where the distribution of the i.i.d. errors is completely unknown outside a specified interval, an asymptotically optimal robust M-estimator of the regression parameter vector is constructed. We study a variety of initial values for the iterative computation of this estimator, its finite sample properties are investigated by simulation, and it is compared with estimators that appear elsewhere in the literature. This research somewhat improves part of the work of Collins et al. (1986) who (essentially) assumed that the rows of the design matrix contain repetitions.