An air bearing slider for supporting a transducer is provided with a pair of rails having an air bearing surface with a continuously curved part with its greatest width at the leading end of the slider. In the rear area of the slider the air bearing surfaces are of equal width. The invention furthermore provides a mechanical grinding process using a grinding wheel having two grinding disks separated by a spacer disk and provided with bevelled grinding surfaces on its inner sides. Either by advancing the turning grinding wheel parallel to the surface of the slider from the trailing towards the leading end up to a certain point or in accordance with another embodiment by tilting the slider slightly towards the advance motion and continuously advancing the grinding wheel, the continuously curved air bearing surface portions are provided in a simple and efficient manner.