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Let $f : X \rightarrow Y$ be a genuinely ramified map between irreduciblesmooth projective curves defined over an algebraically closed field. Let $P$ bea branch data on $Y$ such that $P(y)$ and $B_f(y)$ where $B_f$ is branch datafor $f$ are linearly disjoint for every $y \in, Y$. Further assume that either$P$ is tame or $f$ is Galois. Then the pullback, by $f$, of any stableparabolic bundle on $Y$ with respect to $P$ is actually a stable parabolicbundle on $X$ with respect to $f^*P$.

Genuinely ramified maps and stability of pulled-back parabolic bundles