A magnetic head for stretch surface recording SSR includes a floating head slider having a facing surface formed as a part of a spherical surface, wherein a radius R of said spherical surface is given by 80 mm.ltoreq.R.ltoreq.100 mm, the facing surface as viewed from a magnetic recording medium is in the shape of a rectangle having an overall length L along the air flow of 3 mm or less and a transverse width W in a direction normal to the air flow of about 2 mm or less, and wherein at least two longitudinal grooves each having a width w given by 100 .mu.m.ltoreq.w.ltoreq.500 .mu.m are formed on the facing surface extending along the air flow. Floating stability at a high frequency range of 1 to 14 MH.sub.2 is achieved.