  In this paper, we explicitly construct a series of projectors on integral
noncommutative orbifold $T^2/Z_4$ by extended $GHS$ constrution. They include
integration of two arbitary functions with $Z_4$ symmetry. Our expressions
possess manifest $Z_{4}$ symmetry. It is proved that the expression include all
projectors with minimal trace and in their standard expansions, the eigen value
functions of coefficient operators are continuous with respect to the arguments
$k$ and $q$. Based on the integral expression, we alternately show the
derivative expression in terms of the similar kernal to the integral one.Since
projectors correspond to soliton solutions of the field theory on the
noncommutative orbifold, we thus present a series of corresponding solitons.
