Two-dimensional principal component analysis (2DPCA), as a state-of-the-art method for dimensionality reduction, has been widely used in face recognition. However, it is very sensitive to outliers since it minimizes the sum of squared F-norm, which is least-squares loss in nature. Recently, angle 2DPCA was presented to alleviate this problem by minimizing the sum of Fnorm, which is corresponding to L1 loss. But a vital unresolved problem of angle 2DPCA is that it needs many more coefficients for image representation because it works only in the row direction. In this letter, we first give a new angle 2DPCA called Sin-2DPCA by minimizing the relative error, which has a better explanation than the original one. Furthermore, in order to obtain better performance with fewer reduced coefficients, we project the input image to a lower dimension from right and left simultaneously, and then, the bilateral angle 2DPCA (BA2DPCA) is proposed. The experimental results on two benchmark face recognition datasets with outlier noises illustrate that the Sin-2DPCA has the similar performance with original angle 2DPCA, and BA2DPCA can obtain the highest performance in all compared algorithms with the minimal number of representation coefficients.