  We develope a local theory for frames on finite dimensional Hilbert spaces.
In particular, a bounded frame on a finite dimensional Hilbert space contains a
subset which is a good Riesz basis for a percentage (arbitrarily close to one)
of the space. We also construct a normalized frame for a Hilbert space which
contains a subset which is a Schauder basis for H but does not contain any
subset which is a Riesz basis for H.
