Observations of X‐ray emissions from binary systems have always been considered important tools to test the validity of General Relativity in strong‐field regimes. The pairs and triplets of high frequency quasi‐periodic oscillations observed in binaries containing a black hole candidate, in particular, have been proposed as a means to measure more directly the black hole properties such as its mass and spin. Numerous models have been suggested over the years to explain the QPOs and the rich phenomenology accompanying them. Many of these models rest on a number of assumptions and are at times in conflict with the most recent observations. We here propose a new, simple model in which the QPOs result from basicp‐mode oscillations of a non‐Keplerian disc of finite size. We show that within this new model all of the key properties of the QPOs:a)harmonic ratios of frequencies even as the frequencies change;b)variations in the relative strength of the frequencies with spectral energy distribution and with photon energy;c)small and systematic changes in the frequencies, can all be explained simply given a single reasonable assumption. © 2004 American Institute of Physics