  A new efficient orthogonalization of the B-spline basis is proposed and
contrasted with some previous orthogonalized methods. The resulting orthogonal
basis of splines is best visualized as a net of functions rather than a
sequence of them. For this reason, the basis is referred to as a splinet. The
splinets feature clear advantages over other spline bases. They efficiently
exploit 'near-orthogonalization' featured by the B-splines and gains are
achieved at two levels: locality that is exhibited through small size of the
total support of a splinet and computational efficiency that follows from a
small number of orthogonalization procedures needed to be performed on the
B-splines to achieve orthogonality. These efficiencies are formally proven by
showing the asymptotic rates with respect to the number of elements in a
splinet. The natural symmetry of the B-splines in the case of the equally
spaced knots is preserved in the splinets, while quasi-symmetrical features are
also seen for the case of arbitrarily spaced knots.
