This article presents a novel iterative algorithm based on Non-negative Matrix Factorisation (NMF) that is particularly well suited to the task of automatic music transcription (AMT). Compared with previous NMF based techniques, this one does not aim at factorizing the timefrequency representation of the entire musical signal into a combination of the possible set of notes. Instead, the proposed algorithm proceeds iteratively by initially decomposing a part of the time-frequency representation into a combination of a small subset of all possible notes then reinvesting this information in the following step involving a large subset of notes. Specifically, starting with the lowest octave of notes that is of interest, each iteration increases the set of notes under consideration by an octave. The resolution of a lower dimensionality problem used to properly initialize matrices for a more complex problem, results in a gain of some percent in the transcription accuracy.