Any set of functions for this new definition of orthogonality?

Question

The set of functions $\phi_k, k\in\mathbb{Z}$ are orthonormal iff $$\int_{-\infty}^\infty\phi_m(t)\phi_n^\ast(t)dt=\delta_{mn}.$$ For example $\phi_m(t)=\mbox{sinc}(t-m)$ is an example of a family of orthonormal functions. Now my question is that is there a set of (infinit many) functions, denote them $\phi_i(t)$, such that $$\int_{-\infty}^\infty\phi_k(t)\phi_m(t)\phi_\ell^\ast(t)\phi_n^\ast(t)dt=\delta_{km}\delta_{\ell n}?$$