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Subspace decomposition has proven to be an important tool in adaptive signal processing. A number of algorithms have been proposed for tracking the dominant subspace. Among the most robust and most efficient methods is the projection approximation and subspace tracking (PAST) method. This paper elaborates on an orthonormal version of the PAST algorithm for fast estimation and tracking of the principal subspace or/and principal components of a vector sequence. The orthonormal PAST (OPAST) algorithm guarantees the orthonormality of the weight matrix at each iteration. Moreover, it has a linear complexity like the PAST algorithm and a global convergence property like the natural power (NP) method.