The paper presents magnetoresistivity measurements in the vortex liquid phase of YBaCuO single crystals with different angles between unidirected twins and current direction in magnetic fields up to 12 T. Unidirected twin planes are the cause of anisotropic pinning of vortices. In contrast with the measurements of the usual longitudinal magnetoresistance of the isotropic sample which is even with respect to reversal of the direction of the magnetic field, we have observed an additional, odd with respect to reversal of the magnetic field, contribution to the longitudinal resistivity which is due to the presence of unidirected twins in the YBaCuO crystals. A theoretical discussion of the effect is presented.