The study of the excitation spectrum of I2 induced by laser radiation near the dissociation limit of the B state enables us to determine the molecular constants of the vibrational levels v′ = 78, 79 and 80; the latest being situated only 1.6 cm−1 from the dissociation limit. The molecular constants are now in good agreement with theoretical predictions. Revised values of the dissociation limits of the B and X state are proposed: they are 20043.176 ± 0.016 and 12440.200 ± 0.020 cm−1 respectively. The excitation spectrum from 20022 to 20039.5 cm−1 is entirely reproduced, together with the assignments and the wavenumbers of all observed lines, principally for calibration purposes.