It is shown that the JackelsGuTruhlar projection technique for computing harmonic frequencies along the intrinsic reaction path is equivalent to use of a new, enormously broad family of the so-called hyperplanar-vibrational-surface (HVS) reaction coordinates, namely, for any arbitrarily chosen set of internal variables , the appropriate HVS reaction coordinate, s, is implicitly defined via the requirement that it remains constant on any so-called orthogonal-to-path hyperplane in the coordinate space spanned by variables . It is proven that s defined in such a way satisfies the local HofackerMarcus conditions and therefore there is no linear term in a Taylor expansion of the potential in terms of vibrational coordinates Q. Since the transformation from Q and s to is explicitly defined, one can use a standard technique to account for potential anharmonicities along the reaction path.