  I investigate dense coding with a general mixed state on the Hilbert space
$C^{d}\otimes C^{d}$ shared between a sender and receiver. The following result
is proved. When the sender prepares the signal states by mutually orthogonal
unitary transformations with equal {\it a priori} probabilities, the capacity
of dense coding is maximized. It is also proved that the optimal capacity of
dense coding $\chi ^{*}$ satisfies $E_{R}(\rho)\leq \chi ^{*}\leq E_{R}(\rho
)+\log_{2}d$, where $E_{R}(\rho)$ is the relative entropy of entanglement of
the shared entangled state.
