A composite perpendicular recording media consisting of magnetically hard and soft regions within each grain is proposed. Application of applied field initially causes the magnetization of the soft region to rotate and, thus, change the angle of the effective field applied to the hard region. This important change in the effective field is enabled by an exchange layer that moderates the interaction between the two regions. Energy arguments show that the resulting performance (as measured by the ratio of energy barrier to switching field) is similar to the previously proposed tilted media, while avoiding some of the difficulties. In particular, fabrication of the proposed composite media appears to be significantly easier than that of tilted media.