F. Gesztesy and B. Simon On Local Borg-Marchenko Uniqueness Results (49K, LaTeX) ABSTRACT. 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