By using a two-color dip spectroscopy, we measured the fluorescence intensity from tryptophan in a water solution. The fluorescence intensity exponentially decreased as the laser intensity for the S n ←S 1 excitation increased. The phenomenon was analyzed by a rate-equation for a three-state model. The analysis shows that tryptophan with the S n state has a radiationless relaxation process without any process through the S 1 state, and that the S n →S 1 internal conversion does not have a 100% yield. The branching ratio of the process is estimated to be 20%. The presented result clarifies in detail the real meaning of Kasha’s rule.