  In this paper, we prove that for any $C^1$ surface diffeomorphism $f$ with
positive topological entropy, there exists a diffeomorphism $g$ arbitrarily
close (in the $C^1$ topology) to $f$ exhibiting a horseshoe $\Lambda$, such
that the topological entropy of $g$ restricted on $\Lambda$ can arbitrarily
approximate the topological entropy of $f$. This extends the Theorem
\cite[Theorem 1.1]{Gan} of Gan.
