  Given a set $\cal P$ of points in the Euclidean plane and two triangulations
of $\cal P$, the flip distance between these two triangulations is the minimum
number of flips required to transform one triangulation into the other.
Parameterized Flip Distance problem is to decide if the flip distance between
two given triangulations is equal to a given integer $k$. The previous best FPT
algorithm runs in time $O^{*}(k\cdot c^{k})$ ($c\leq 2\times 14^{11}$), where
each step has fourteen possible choices, and the length of the action sequence
is bounded by $11k$. By applying the backtracking strategy and analyzing the
underlying property of the flip sequence, each step of our algorithm has only
five possible choices. Based on an auxiliary graph $G$, we prove that the
length of the action sequence for our algorithm is bounded by $2|G|$. As a
result, we present an FPT algorithm running in time $O^{*}(k\cdot 32^{k})$.
