A novel of β-Divergence for nonnegative matrix factorization two-dimensional (NMF2D) with sparseness constraints is proposed in this paper. This research focuses on biomedical signal separation, which denotes a separation on the mixture of heart sound and lung sound. Initially, a mixture of heart sound and lung sound has been decomposed into an independent signal, which is an estimated heart sound signal and estimated lung sound signal. The spectrum of independent signal is modelled based on 2 dimensions, which are the temporal code and the spectral basis by using β-Divergence NMF2D algorithm with sparseness constraints. The algorithm has been updated multiplicative and iteratively via multiplicative update rules (MU rules). β-Divergence with sparseness constraints allows minimization on the vagueness of source model to be completed and oneness has been applied to it. Then, estimation of each separated audio has been analyzed via comparison with the original heart sound and lung sound signal in term of Signal-to-Distortion Ratio (SDR).