Block principal component analysis with ℓ₁-norm (BPCA-L1) has demonstrated its effectiveness in a lot of visual classification and data mining tasks. However, the greedy strategy for solving the ℓ₁-norm maximization problem is prone to being struck in local solutions. In this paper, we propose a BPCA with nongreedy ℓ₁-norm maximization, which obtains better solutions than BPCA-L1 with all the projection directions optimized simultaneously. Other than BPCA-L1, the new algorithm has been evaluated against some popular principal component analysis (PCA) algorithms including PCA-L1 and 2-D PCA-L1 on a variety of benchmark data sets. The results demonstrate the effectiveness of the proposed method.