A novel space vector modulation scheme for a five-to-three phase conventional matrix converter (CMC) is proposed. This modulation scheme is able to increase the voltage transfer ratio to 0.8921 and also ensures vector elimination in the d2–q2 vector space in order to ensure a high quality input current waveform for a reference balanced sinusoidal three-phase output. By utilizing both the large and small space vectors in the input current vector spaces, additional degrees of freedom are obtained which in turn allows the proposed scheme to control the vectors in the d2–q2 vector space. A two-step commutation scheme is implemented to reduce commutation complexity and minimize switching losses. The operation of the proposed modulation scheme has been confirmed by simulation results and harmonic analysis has been performed on the input currents, output voltages, and output currents. The maximum voltage transfer ratio is shown to be higher than an equivalent three-to-three-phase CMC while ensuring d2–q2 vector elimination.