  Let X be a smooth projective curve of genus g>1 over an algebraically closed
field of characteristic 2. Pull-back by the (absolute) Frobenius on X only
defines a rational morphism on the moduli scheme of rank-2 vector bundles on X,
because the Frobenius pull-back may destory stability of a vector bundle. This
paper introduces and studies a Harder-Narasimhan type stratification on the
moduli scheme and proves that the family of semi-stable rank-2 vector bundles
(with a fixed degree) whose Frobenius pull-back are not semi-stable is
parameterized by an irreducible subscheme of dimension 3g-4.
