Self-handover, transferring an object between one's own hands, is a common but understudied bimanual action. While it facilitates seamless transitions in complex tasks, the strategies underlying its execution remain largely unexplored. Here, we introduce the first systematic taxonomy of self-handover, derived from manual annotation of over 12 hours of cooking activity performed by 21 participants. Our analysis reveals that self-handover is not merely a passive transition, but a highly coordinated action involving anticipatory adjustments by both hands. As a step toward automated analysis of human manipulation, we further demonstrate the feasibility of classifying self-handover types using a state-of-the-art vision-language model. These findings offer fresh insights into bimanual coordination, underscoring the role of self-handover in enabling smooth task transitions-an ability essential for adaptive dual-arm robotics.