Exact sequence of stable vector bundles on projective curves

Let X be a smooth complex projective curve of genus g over an algebraically closed field k of charcteristic 0. In this paper we prove that given two general stable bundles F and G such that 0 < mu(G) - mu(F) less than or equal to g-1/max{rank G, rank F} there exists an extension (0.1) 0 --> F --> E --> G --> 0 of G by F with E stable. Moreover, such extension also exists for any general stable bundles of F and G of degree even and X either a double covering of a curve of genus 2 or a curve of genus g greater than or equal to 3 + 4(rank G + rank F) + max{rank G, rank F}. That solves LANGE's conjecture ([L2], p. 455) for such cases.