An important property of the three-point functions generated in the early universe is the so-called consistency condition. According to the condition, in the squeezed limit wherein the wave number of one of the three modes (constituting the triangular configuration of wave vectors) is much smaller than the other two, the three-point functions can be completely expressed in terms of the two-point functions. It is found that while the consistency condition is mostly satisfied by the primordial perturbations generated in the inflationary scenario, it is often violated in the bouncing models. The validity of the consistency condition in the context of inflation can be attributed to the fact that the amplitude of the scalar and tensor perturbations freezes on super-Hubble scales. Whereas, in the bouncing scenarios, the amplitude of the scalar and tensor perturbations often grows rapidly as one approaches the bounce, leading to a violation of the condition. In this work, with the help of a specific example involving the tensor perturbations, we explicitly show that suitable nonminimal couplings can restore the consistency condition even in the bouncing models. We briefly discuss the implications of the result. © 2020 American Physical Society.