The breakdown of the Schmid law in bcc metals has been known for a long time. The asymmetry of shearing in the slip direction < 111 > in the positive and negative sense, respectively, commonly identified with the twinning-antitwinning asymmetry, is undoubtedly one of the reasons. However, effect of stress components other than the shear stress in the slip direction may be important. In this paper we investigate by atomistic modeling the effect of shear stresses perpendicular to the Burgers vector on the glide of a/2 < 111 > screw dislocations. We show that these shear stresses can significantly elevate or reduce the critical resolved shear stress (CRSS) in the direction of the Burgers vector needed for the dislocation motion, i.e. the Peierls stress. This occurs owing to the changes of the core induced by these stresses. This effect may be the reason why slip systems with smaller Schmid factors may be preferred over that with the largest Schmid factor.