  Based on maximally entangled states in the full- and sub-spaces of two
qutrits, we present an alternative decomposition of two-qutrit pure states in a
form $|\Psi>=\frac{p_{1}}{\sqrt{3}}(|00>+|11>+|22>)
+\frac{p_{2}}{\sqrt{2}}(|01>+|12>)+ p_{3}e^{i\theta}|02>$. Similar to the
Schmidt decomposition, all two-qutrit pure states can be transformed into the
alternative decomposition under local unitary transformations, and the
parameter $p_1$ is shown to be an entanglement invariant.
