The discrete time channel AWGN(A) with additive white Gaussian noise, strict power constraint and noiseless feedback is considered. The best error decoding exponent is investigated, limiting to the case of non-exponential number of messages (i.e. the rate of transmission R = 0). The new transmission strategy is proposed, showing that for AWGN(A) channel with noiseless feedback at zero rate R = 0 it is possible to achieve the same error exponent as for transmission of two messages. It gives another proof of known result for AWGN(A) channel. The strategy described is applicable to a wider class of channels.