We propose a novel speech enhancement algorithm, termed improved global soft decision (IGSD). IGSD is a unified framework for global soft decision on speech absence/presence, noise spectrum estimation, spectral gain modification based on Ephraim-Malah noise suppression. In IGSD, speech absence probability (SAP) is the most important factor, and we propose an efficient and novel SAP estimation in which the SAP is derived based on the general hypothesis for speech absence/presence. In IGSD, the global SAP based on the global hypothesis for speech absence/presence is used to prevent from the problem caused by insufficient amount of data, but more general hypothesis is utilized in the derivation of global SAP estimation. The performance of IGSD is evaluated both subjectively and objectively, and the quality of speech is improved significantly, compared with conventional GSD speech enhancement algorithm.