Inspired by the advent of bi-unique range sets [2], we obtain a new bi-unique range sets, with smallest cardinalities ever for the derivatives of meromorphic functions which improves all the results obtained so far in some sense including a result of Banerjee-Bhattacharjee [4]. Furthermore at the last section we pose an open question for future research.

Tbilisi Mathematical Journal, Vol. 9(2) (2016), pp. 1-13