The orientation tuning properties of the non-classical receptive field (nCRF or "surround") relative to that of the classical receptive field (CRF or "center") were tested for 119 neurons in the cat primary visual cortex (V1). The stimuli were concentric sinusoidal gratings generated on a computer screen with the center grating presented at an optimal orientation to stimulate the CRF and the surround grating with variable orientations stimulating the nCRF. Based on the presence or absence of surround suppression, measured by the suppression index at the optimal orientation of the cells, we subdivided the neurons into two categories: surround-suppressive (SS) cells and surround-non-suppressive (SN) cells. When stimulated with an optimally oriented grating centered at CRF, the SS cells showed increasing surround suppression when the stimulus grating was expanded beyond the boundary of the CRF, whereas for the SN cells, expanding the stimulus grating beyond the CRF caused no suppression of the center response. For the SS cells, strength of surround suppression was dependent on the relative orientation between CRF and nCRF: an iso-orientation grating over center and surround at the optimal orientation evoked strongest suppression and a surround grating orthogonal to the optimal center grating evoked the weakest or no suppression. By contrast, the SN cells showed slightly increased responses to an iso-orientation stimulus and weak suppression to orthogonal surround gratings. This iso-/orthogonal orientation selectivity between center and surround was analyzed in 22 SN and 97 SS cells, and for the two types of cells, the different center-surround orientation selectivity was dependent on the suppressive strength of the cells. We conclude that SN cells are suitable to detect orientation continuity or similarity between CRF and nCRF, whereas the SS cells are adapted to the detection of discontinuity or differences in orientation between CRF and nCRF.