I argue that the slowly expanding biconical structure of the Red Rectangle-a nebula around the post-asymptotic giant branch binary stellar system HD 44179-can be formed by intermittent jets blown by the accreting companion. The bright biconical structure of the Red Rectangle nebula can be understood to be composed of a multiple double-ring system. In the proposed shaping process, one among several processes through which a companion can shape the circumbinary gas, the companion accretes mass from the slow wind blown by the evolved mass-losing star. An accretion disk is formed, and if mass accretion is larger than a critical value, two jets, or a collimated fast wind, are blown. If the high mass loss rate duration is long, bipolar lobes are formed. If, on the other hand, the mass-loss rate is intermittent and during one orbital period the slow wind fills a region that does not extend much beyond the binary system, then only a fraction of the double-lobe structure is formed, namely, rings. This, I propose, was the case with the progenitor of the Red Rectangle, where intermittent episodes of enhanced mass-loss rate led to the formation of a multiple double-ring system.