  Here we consider perfect entanglers from another perspective. It is shown
that there are some {\em special} perfect entanglers which can maximally
entangle a {\em full} product basis. We have explicitly constructed a
one-parameter family of such entanglers together with the proper product basis
that they maximally entangle. This special family of perfect entanglers
contains some well-known operators such as {\textsc{cnot}} and
{\textsc{dcnot}}, but {\em not} ${\small{\sqrt{\rm{\textsc{swap}}}}}$. In
addition, it is shown that all perfect entanglers with entangling power equal
to the maximal value, 2/9, are also special perfect entanglers. It is proved
that the one-parameter family is the only possible set of special perfect
entanglers. Also we provide an analytic way to implement any arbitrary
two-qubit gate, given a proper special perfect entangler supplemented with
single-qubit gates. Such these gates are shown to provide a minimum universal
gate construction in that just two of them are necessary and sufficient in
implementation of a generic two-qubit gate.
