A novel subspace method is proposed for part-based face recognition by using non-negative matrix factorization with sparseness constraints (NMFs) and Fisher's linear discriminant (FLD) hence its abbreviation, FNMFs. A comparative analysis engages PCA+FLD (FPCA) method and FNMFs method for both part-based and holistic-based face recognition. The comparative experiments are completed for the ORL face database and UMIST face database, it shows that FNMFs has better performance than FPCA-based method both for holistic-face and parts-face images recognition.