Summary: We introduce some projection-invariants for a normalized sequence in a Hilbert space, based on the smallness of the mutual projections of its elements. We then establish conditions to have the original sequence equivalent to its Gram-Schmidt orthonormalization. In many problems of wavelet-decomposition and reconstruction, the use of orthogonal bases cannot be implemented in the construction of certain filters and other practical features. Then, a quasiorthonormal structure for representation may be the next best alternative by achieving new constraints while we can still arbitrarily approximate the powerful classical orthogonal results.