This paper introduces a fast implementation of the power iterations method for subspace tracking, based on an approximation less restrictive than the well known projection approximation. This algorithm guarantees the orthonormality of the estimated subspace weighting matrix at each iteration, and satisfies a global and exponential convergence property. Moreover, it outperforms many subspace trackers related to the power method, such as PAST, NIC, NP3 and OPAST, while keeping the same computational complexity.