The method of artificial neural networks (ANNs) and the method of principal components are considered jointly as applied to remote sounding of vertical profiles of temperature and atmosphere composition. A modification of the ANN method based on minimization of the root-mean-square error of the final determined parameter of the atmosphere is proposed. The significant (by a factor of hundreds) advantage of the proposed technique as applied to the rate of ANN learning and a little advantage in the accuracy of the profile determination are demonstrated by an example of determining the vertical profile of temperature by measurements with an MTVZA device.