In this letter, we present a new algorithm for the harmonic and percussive separation of jazz music. Using a short-time Fourier transform and nonnegative matrix factorization, the signal is decomposed into rank components. Each component is then split into harmonic and percussive parts using masks calculated based on their tonalities. Finally, the harmonic and percussive parts are separated after applying the masks and a summation. We evaluate the algorithm based on real audio examples using both objective and subjective assessments. The proposed algorithm performs well for the separation of harmonic and percussive parts of jazz excerpts.