Whitened Neural Network (WNN) is a recent advanced deep architecture, which improves convergence and generalization of canonical neural networks by whitening their internal hidden representation. However, the whitening transformation increases computation time. Unlike WNN that reduced runtime by performing whitening every thousand iterations, which degenerates convergence due to the ill conditioning, we present generalized WNN (GWNN), which has three appealing properties. First, GWNN is able to learn compact representation to reduce computations. Second, it enables whitening transformation to be performed in a short period, preserving good conditioning. Third, we propose a data-independent estimation of the covariance matrix to further improve computational efficiency. Extensive experiments on various datasets demonstrate the benefits of GWNN.