Abstract: In sparse representation theory, how to construct a dictionary and update dictionary making the dictionary discriminative is still an open problem. In order to solve this problem, a dictionary learning method was presented based on relationship between atoms and labels and a matrix was built based on the relationship between them. Then the matrix was updated with the update of the dictionary atoms. The adaptive relationship between atoms and labels of the matrix was constructed, improves the discriminant ability of dictionary, the necessary guarantee for the classification was provided later. This method not only avoided the poor discriminant ability of the share dictionary, but also avoided the individual training dictionary method taking up lots of time and memory faults. And making use of l ₂₁ norm constraining residual to remove noise, can not only deal with sparse noise, but also the non-sparse noise, which is robust to the noise. The experiment results show that the proposed method has robustness and high recognition rate compared with other dictionary learning methods.