Apparatus and a method for positioning a flexible magnetic recording medium, such as a floppy disk, (12; 112), in such a way as to permit magnetic means (14; 162) on opposed sides of the medium to orient the particles in the magnetic coatings on the medium immediately after the coatings have been applied to the medium and as the medium is rotated. In one embodiment, the apparatus includes stabilizing devices (22) which are located at circumferentially spaced locations about the outer periphery of the medium (12) when the medium is mounted for rotation. Each device comprises a pair of substantially J-shaped, wire-like members (38) arranged to define a gap (46) between which the outer peripheral margin of the medium (12) passes. The J-shaped members (38) can be tubular or solid. If tubular, they can be used direct fluid under pressure onto the opposite sides of the medium as the medium rotates. In a second embodiment, a pair of bowl-shaped members (125,126) are hingedly mounted together and moved into face-to-face relationship with each other but are spaced apart to present an outer peripheral, continuous gap (128) which receives the outer peripheral margin of the medium (112) when the medium is rotatably mounted on one of the bowl-shaped members. Air is directed into the interiors of the bowl-shaped members and then outwardly therefrom through the gap on opposite sides of the medium to provide Venturi effect to keep the outer peripheral margin of the medium centered in the gap and stabilized against deviation out of the plane of rotation of the medium.