Finite size scale invariance

We develop a new approach to scale symmetry, which takes into account the p ossible finite cutoffs of the fields or the parameters. This new symmetry, called finite size scale symmetry: i) includes the traditional self-similar ity as a limiting case, when the cut-offs are set to infinity (infinite siz e-system); ii) is consistent with the traditional finite size scaling appro ach already used in critical phenomena; iii) enables the computation of som e of the universal functions appearing in the finite size scaling formulati on, iv) allows scale transformations leaving the cut-offs invariant, like i n the traditional renormalization approach, v) can be formulated to allow f or positive or negative fields and parameters; vi) leads to new predictions about the shape of some distributions in critical phenomena or turbulence which are in very good agreement with the experimental or numerical finding s.