Whitening is a preprocessing method that can remove the correlation between variables of data. Two-dimensional whitening reconstruction （TWR） is a new whitening method for a single image. In this paper， we will elaborate the equivalence between TWR and column-based ZCA whitening， that is， TWR can remove the correlation in image column. However， the correlation within the local block of the image is often much greater than that within the column. From the perspective of removing the correlation within the local block of the image， this paper proposes two improved TWR methods： reshaped-based TWR （RTWR） and patch-based TWR（PTWR）. RTWR firstly reshapes an image to form a new matrix of which each column vector corresponds to the sub-block of the original image， and then performs the TWR on the reshaped matrix. In PTWR method， TWR is directly applied to each sub-block of the image. The experimental results on ORL， CMU PIE and AR face datasets show that RTWR and PTWR are more beneficial to improving the subsequent classification performance than TWR.