A magnetic head for perpendicular recording without writing from the lateral sides of a mains pole and without erasing data on adjacent tracks. A magnetic disk storage apparatus using the magnetic head. The lateral side of the main pole of a magnetic head for perpendicular recording may have an inverted tapered shape obtained by forming a groove as a track portion to an inorganic insulating layer and then forming a magnetic layer and then flattening the upper surface. A leading edge, a trailing edge, or both lateral edges of the magnetic head may be tapered. The taper may be either smooth and linear or curved in profile.