We report unusual photophysical properties observed on two newly designed 3-hydroxychromone derivatives exhibiting the excited-state intramolecular proton transfer (ESIPT) reaction. The efficiency of ESIPT reaction is greatly enhanced upon excitation with high energy quanta to S_n (n > 1) levels in low-polarity solvents. Based on detailed analyses of excitation and emission spectra as well as time-resolved emission kinetics we derive that conditions, in which this phenomenon contradicting Kasha's rule is observed, are quite different from that for observation of anti-Kasha emission.