A floating magnetic head having a magnetic head core incorporated in a non-magnetic slider of a cubic configuration. The core is disposed perpendicular to the plane of a magnetic disk. The core is bonded by glass to the slider at one side of the core facing the magnetic disk, and also is bonded by a resin or bonding material to the slider at the other side of the core remote from the magnetic disk. A resin or an adhesive tape is applied to the back surface of the slider, supported by a support member, at a predetermined ratio of the resin or the adhesive tape to the area of the back surface. It is effective to bond the support member to the back surface of the slider by adhesives applied to that portion of the back surface greater than the point of bonding between the support member and the back surface.