ICN is one of the few simple triatomic molecules whose photo dissociation mechanisms have been thoroughly investigated. Since it has a linear structure in the electronic ground state, the dissociation follows a photoexcitation at a linear or slightly bent structure. It is generally believed that the (A) over tilde -band consists of the dominant excitation to (3)Pi(0+) (4A') with the transition dipole moment (TDM) parallel to the molecular axis (z), a slightly weaker transition to (1)Pi(1), (5A', 4A ''), and a much weaker transition to (3)Pi(1), (3A', 2A ''), both of the latter two having perpendicular TDMs. In the present work, we have theoretically studied the geometry dependence of these TDMs and found a pronounced theta (bending angle) dependence in the parallel (z) component of the TDMs to (1)Pi(1) (5A') and (3)Pi(1), (3A'), both of which should be zero at a linear geometry by symmetry and thus have been previously ignored. We estimated that the z component TDM to (1)Pi(1) (5A') has a contribution of 15-20% to the total absorption cross-section at 249 nm at room temperature. Interestingly, the TDM to (3)Pi(0+) (4A') does not exhibit such theta dependency and thus has only the z component. We compare the TDMs of ICN and CH3I molecules having similar excited states. The fact that all the TDMs to 3A', 4A', and SA' have nonnegligible z components implies the importance of the coherent excitation contributions to various observables of CN fragment, such as the anisotropy parameter, the orientation parameter, and the rotational level distribution as well as the rotational fine structure level distribution.