Aiming at the problem of the error existed from the hidden layer to the output layer of Extreme Learning Machine(ELM), it was found the analysis revealed that the error came from the process of solving the Moore-Penrose generalized inverse matrix H ^† of the hidden layer output matrix H,that revaled the matrix H ^† H was deviated from the identity matrix. The appropriate output matrix H was able to be selected according to the degree of deviation to obtain a smaller training error. According to the definitions of the generalized inverse matrix and auxiliary matrix,the target matrix H ^† H and the error index L21-norm were firstly determined. Then,the experimental analysis showed that the L21-norm of H ^† H was linearly related to the ELM error. Finally,Gaussian filtering was introduced to reduce the noise of the target matrix,which effectively reduced the L21-norm of the target matrix and the ELM error,achieving the purpose of optimizing the ELM algorithm.