  We introduce a new method for the computation of the transition moments
between the excited electronic states based on the expectation value formalism
of the coupled cluster theory [B. Jeziorski and R. Moszynski, Int. J. Quant.
Chem. 48, 161 (1993)]. The working expressions of the new method solely employ
the coupled cluster amplitudes. In the approximation adopted in the present
paper the cluster expansion is limited to single, double, and linear triple
excitations. The computed dipole transition probabilities for the
singlet-singlet and triplet-triplet transitions in alkali earth atoms agree
well with the available theoretical and experimental data. In contrast to the
existing coupled cluster response theory, the matrix elements obtained by using
our approach satisfy the Hermitian symmetry even if the excitations in the
cluster operator are truncated. As a part of the numerical evidence for the new
method, we report calculations of the transition moments between the excited
triplet states which have not yet been reported in the literature within the
coupled cluster theory. Slater-type basis sets constructed according to the
correlation-consistency principle are used in our calculations.
