This paper proposes a novel and computationally efficient selective harmonic elimination (SHE) technique which eliminates the predefined lower order harmonics (till 19th order) from the phase voltage while controlling its fundamental. In conventional SHE schemes, the notch angles need to be computed online for each frequency in order to eliminate the harmonics and control the fundamental value. This involves intensive online computations and the convergence to the correct notch angles is not guaranteed, resulting in incorrect fundamental and/or presence of lower order harmonics. In contrast to this, a SHE technique, that uses the same pre-computed notch angles for all modulation indices, is proposed in this paper, thereby significantly reducing the computational burden. Here, the control of fundamental voltage at different frequencies is ensured by the concept of phase shifting of two identical notched waveforms. This ensures precise control of fundamental voltage while completely eliminating the pre-defined lower order harmonics. Moreover, the proposed scheme exhibits linear control till 0.582 times the DC-link voltage compared to 0.577 times the DC-link voltage in case of space vector PWM. The proposed method is validated experimentally on an induction motor drive system.