  In this paper we define "piecewise scalable frames". This new scaling process
allows us to alter many frames to Parseval frames which is impossible by the
previous standard scaling. We give necessary and sufficient conditions for a
frame to be piecewise scalable. We show that piecewise scalability is preserved
under unitary transformations. Unlike standard scaling, we show that all frames
in $\RR^2$ and $\RR^3$ are piecewise scalable. We also show that if the frame
vectors are close to each other, then they might not be piecewise scalable.
Several properties of scaling constants are also presented.
