We investigate the pump/probe femtosecond spectroscopy of a diatomic molecule which is ionized by the absorption of a photon from the probe laser pulse. As a realistic example, an electronic transition of the sodium dimer is investigated. The dependence of the total ion signal on the delay time between the pump and probe pulse is studied for different frequencies of the ionizing laser. Also, non-Condon effects are shown to be important under certain conditions.