  Entanglement transformation of composite quantum systems is investigated in
the context of group representation theory. Representation of the direct
product group $SL(2,C)\otimes SL(2,C)$, composed of local operators acting on
the binary composite system, is realized in the four-dimensional complex space
in terms of a set of novel bases that are pseudo orthonormalized. The
two-to-one homomorphism is then established for the group $SL(2,C)\otimes
SL(2,C)$ onto the $SO(4,C)$. It is shown that the resulting representation
theory leads to the complete characterization for the entanglement
transformation of the binary composite system.
