  In order to study the pseudo entropy of time-like subregions holographically,
the previous smooth space-like extremal surface was recently generalized to mix
space-like and time-like segments and the area becomes complex value. This
paper finds that, if one tries to use such kind of piecewise smooth extremal
surfaces to compute time-like entanglement entropy holographically, the complex
area is not unique in general. We then generalize the original holographic
proposal of space-like entanglement entropy to pick up a unique area from all
allowed ``space-like+time-like'' piecewise smooth extremal surfaces for a
time-like subregion. We will give some concrete examples to show the
correctness of our proposal.
