Graphics rendering requires various huge amounts of temporary data storages, prohibiting this feature from being implemented on slim embedded devices. To overcome this difficulty, we focus our effort on storage of transparent fragments after rasterization stage. We base our design on the fact that: successive frames typically will have the same or very similar number of transparent fragments located at the same screen pixel location. We propose a history based transparent fragment buffer called H-Buffer. In this design, transparent fragment counts at all pixel locations are collected for every frame, and are used for storage allocation for the next frame. For the unavoidable case of insufficient storage allocation, our overflow storage allocation assigns neighbor located pixel locations to share a given overflow area, in an attempt to reduce internal fragmentation. In evaluation, compared against the strongest competitor, the T-buffer, results show that our method reduces storage pressure by 25% in QUAKE4 benchmark.