Transient luminescence which is attributed to optical transition from excitonic states to the ground states is studied, applying picosecond luminescence techniques to a pyrene crystal. The very fast decaytime (>4 ps) was observed at the shorter wavelengths than 0-0 luminescence band and the same decaytime component was included in the 400 nm-region of luminescence spectrum. A conclusion is drawn that rate of bypass process within free exciton band is larger at higher temperature than at lower temperatures. Transient luminescence emitted during excitons are sliding down on the adiabatic potential energy curve between self-trapping barrier and self-trapped state bottom was observed. Transient luminescence in an alpha-perylene is also briefly discussed.