We formulate a novel loss function, called Angular Sparsemax for face recognition. The proposed loss function promotes sparseness of the hypotheses prediction function similar to Sparsemax with Fenchel-Young regularisation. With introducing an additive angular margin on the score vector, the discriminatory power of the face embedding is further improved. The proposed loss function is experimentally validated on several databases in term of recognition accuracy. Its performance compares well with the state of the art Arcface loss.