Efficient and compact representation of images is a fundamental problem in computer vision. Principal Component Analysis (PCA) has been widely used for image representation and has been successfully applied to many computer vision algorithms. In this paper, we propose a method that uses Haar-like binary box functions to span a subspace which approximates the PCA subspace. The proposed method can perform vector dot product very efficiently using integral image. We also show that B-PCA base vectors are nearly orthogonal to each other. As a result, in the non-orthogonal vector decomposition process, the expensive pseudo-inverse projection operator can be approximated by the direct dot product without causing significant distance distortion. Experiments on real image datasets show that B-PCA has comparable performance to PCA in image reconstruction and recognition tasks with significant speed improvement.