We present the first algorithm for the ({\em black box\/}) interpolation of $t$-sparse, $n$-variate rational functions without knowing bounds on exponents of their sparse representation with the number of queries needed by the algorithm, independent on exponents. In fact, the algorithm uses $O(nt^t)$ queries to the {\em black box\/}, and can be implemented for a fixed $t$ in a polynomially bounded storage (or polynomial parallel time).