We use time- and angle-resolved photoemission spectroscopy to reveal momentum-resolved characteristics of interband transitions in InSb. The transitions along the Γ-K line are correctly described in terms of the independent-quasiparticle band picture up to 1.9 eV. However, the transitions along the Γ-L line turn out to be strongly excitonic above 1.7 eV, associated with the saddle-point excitons at the E1 critical point. The momentum- and energy-resolved spectra of photoionization of the saddle-point excitons show that the wave function is composed of the electron-hole pair states with the wave vector of 0.453±0.055Å-1 along the Γ-L direction of the Brillouin zone. Time-resolved characteristics of the exciton photoionization show that the coherently generated excitonic polarization decays with a time constant of 22 ± 1 fs due to the autoionization from the excitonic state to uncorrelated electron-hole pair states.