Using femtosecond two-color infrared pump-probe spectroscopy, we study the vibrational relaxation of the O-H stretch vibrations of liquid H2O after excitation of the overtone transition. The overtone transition has its maximum at 6900 cm(-1) (1.45 mu m), which is a relatively high frequency in view of the central frequency of 3400 cm(-1) of the fundamental transition. The excitation of the overtone leads to a transient induced absorption of two-exciton states of the O-H stretch vibrations. When the overtone excitation frequency is tuned from 6600 to 7200 cm(-1), the vibrational relaxation time constant of the two-exciton states increases from 400 +/- 50 fs to 540 +/- 40 fs. These values define a limited range of relatively long relaxation time constants compared to the range of relaxation time constants of 250-550 fs that we recently observed for the one-exciton O-H stretch vibrational state of liquid H2O (S. T. van der Post et al., Nature Comm. 2015, 6, 8384). We explain the high central frequency and the limited range of relatively long relaxation time constants of the overtone transition from the destructive quantum interference of the mechanical and electrical anharmonic contributions to the overtone transition probability. As a result of this destructive interference, the overtone transition of liquid H2O is dominated by molecules of which the O-H groups donate relatively weak hydrogen bonds to other H2O molecules.