We present a synthesis procedure for constructing a non-reciprocal phase-insensitive quantum amplifier using quantum optics. An expression is obtained for the corresponding level of noise by this amplifier. This noise level is greater than the level required in a previous paper which did not impose the non-reciprocal requirement. The synthesis procedure uses a singularly perturbed quantum system and leads to an amplifier involving three squeezers and a number of beamsplitters.