In this study, we aim to improve the performance of audio source separation for monaural mixture signals. For monaural audio source separation, semisupervised nonnegative matrix factorization (SNMF) can achieve higher separation performance by employing small supervised signals. In particular, penalized SNMF (PSNMF) with orthogonality penalty is an effective method. PSNMF forces two basis matrices for target and nontarget sources to be orthogonal to each other and improves the separation accuracy. However, the conventional orthogonality penalty is based on an inner product and does not affect the estimation of the basis matrix properly because of the scale indeterminacy between the basis and activation matrices in NMF. To cope with this problem, a new PSNMF with cosine similarity between the basis matrices is proposed. The experimental comparison shows the efficacy of the proposed cosine similarity penalty in supervised audio source separation.