The double transition of a perpendicular medium with no keeper layer was investigated by using a 2D scalar field model. A double transition can be recorded by applying the bipolar field of a ring head. The backward transition at the trailing edge was used for memorizing bit information. The forward transition at the leading edge was overwritten by the backward transition after motion of the medium. The calculations for finding the transition length and the transition center of isolated transition were carried out on the basis of various types of transition modeling. As the result, it was confirmed that the transition length of the backward transition can be narrowed by the magnetostatic field induced by the forward transition even if the head field gradient of the ring head is poor. The calculated input/output curves and roll-off curves were compared with the experimental results, and good agreement was obtained. A complementary single-pole (CSP) head with a bipolar field and high field gradient was proposed as a means of attaining higher-density magnetic recording in a perpendicular medium with no keeper layer.