Due to the wide existence of mixed pixels, the derivation of constituent components (endmembers) and their proportions (abundances) at subpixel scales has become an important research topic. In this paper, we propose a novel unsupervised decomposition method based on the classical maximum entropy principle, termed uMaxEnt. The algorithm integrates a global least square error-based endmember detection and a per-pixel maximum entropy learning to find the most possible proportions. We apply the proposed method to the subject of spectral unmixing. The experimental results obtained from both simulated and real hyper-spectral data demonstrate the effectiveness of the uMaxEnt method