We report for the first time on predominant growth of non-polar a-plane (Al,Ga)N layers on patterned c-plane AlN/sapphire templates with ridges oriented along the Al2O3 direction. The layers were grown by hydride vapor phase epitaxy. During the first stages of the growth (Al,Ga)N nucleates simultaneously on top of the ridges, inside the trenches and on the trench sidewalls. As a result, two different (Al,Ga)N orientations are formed with respect to the horizontal growth front: c-plane (Al,Ga)N on the c-plane ridges as well as inside the trenches and a-plane (Al,Ga)N on the trench sidewalls. The growth rate of a-plane (Al,Ga)N exceeds that of c-plane regions, which leads to the complete overgrowth of c-plane (Al,Ga)N by the a-plane oriented material.