We investigate the possibility of a propagating primary wave decaying into secondary waves through three-wave interactions. Such a possibility exists in an inviscid isothermal atmosphere when the vertical wavelength is small compared to the scale height. Initially, the amplitude of the secondary waves grows exponentially, and this growth time decreases exponentially with height. Initially, the amplitude of the secondary waves grows exponentially, and this growth time decreases exponentially with height. This means that as the primary wave propagates upward its energy is continuously transfered to the secondary waves. This transfer becomes increasingly rapid with increasing height. It is shown that this process can take place even when the local Richardson number is more than 100, indicating dynamic stability.