  We provide a new short proof of the following fact, first proved by one of us
in 1998: If two Weyl-Titchmarsh m-functions, $m_j(z)$, of two Schr\"odinger
operators $H_j = -\f{d^2}{dx^2} + q_j$, j=1,2 in $L^2 ((0,R))$, $0<R\leq
\infty$, are exponentially close, that is, $|m_1(z)- m_2(z)|
\underset{|z|\to\infty}{=} O(e^{-2\Ima (z^{1/2})a})$, 0<a<R, then $q_1 = q_2$
a.e.~on $[0,a]$. The result applies to any boundary conditions at x=0 and x=R
and should be considered a local version of the celebrated Borg-Marchenko
uniqueness result (which is quickly recovered as a corollary to our proof).
Moreover, we extend the local uniqueness result to matrix-valued Schr\"odinger
operators.
