  We initiated the program to look for new and simple forms for the
five-dimensional rotating squashed black holes by solving directly the equation
of motion. In a recent paper, the metric ansatz of dimensional reduction along
the fifth spatial dimension was used to obtain a new but rather simple form for
the five-dimensional rotating uncharged black hole solution with squashed
horizons via solving the vacuum Einstein field equations. In this work, we
continue to seek for another new but relatively simple form for the neutral
rotating squashed black hole solution by using a different metric ansatz of
time-like dimensional reduction. We then find its relation to our previous
solution and investigate its thermodynamics by means of the counterterm method.
Compared with the previous results given by the other author, both of our new
metric forms and their associated thermodynamic expressions are very concise
and elegant. Both of two new forms for the neutral rotating squashed black hole
solution presented in this paper can be used as the seed to generate its
charged generalization in D=5 minimal supergravity.
