  We discuss an effective way for analyzing the system on the magnetized
twisted orbifolds in operator formalism, especially in the complicated cases
$T^{2}/Z_{3}$, $T^{2}/Z_{4}$ and $T^{2}/Z_{6}$. We can obtain the exact and
analytical results which can be applicable for any larger values of the
quantized magnetic flux M, and show that the (non-diagonalized) kinetic terms
are generated via our formalism and the number of the surviving physical states
are calculable in a rigorous manner by simply following usual procedures in
linear algebra in any case. Our approach is very powerful when we try to
examine properties of the physical states on (complicated) magnetized orbifolds
$T^{2}/Z_{3}$, $T^{2}/Z_{4}$, $T^{2}/Z_{6}$ (and would be in other cases on
higher-dimensional torus) and could be an essential tool for actual realistic
model construction based on these geometries.
