  By using the classification of Fano 3-folds we prove: Let $X$ be Fano 3-fold.
Assume that the tangent bundle $T_X$ of $X$ is not stable (i.e. semi-stable or
unstable). Then $b_2\geq 2$ and a relative tangent sheaf $T_{X/Y}$ of a
contraction $f:X\longrightarrow Y$ of an extremal face on $X$ is a
destabilising subsheaf of $T_X$.
