We perform an alternative approach to produce highly unipolar terahertz pulses. The idea is based on the nonuniform amplification of seed ultrashort carrier-envelope phase (CEP) pulses in nonequilibrium fast relaxing plasma of air or nitrogen. If the gain coefficient drops significantly within the duration of a one-cycle CEP pulse, it undergoes significant distortion where the leading edge of the pulse is amplified and the trailing tail of opposite polarity is absorbed. The obtained results involve a self-consistent solution of the second-order wave equation and kinetic Boltzmann equation for the electron velocity distribution function relaxation.