Consistent Batalin-Fradkin quantization of infinitely reducible first class constraints

We reconsider the problem of Becchi-Rouet-Stora-Tyutin (BRST) quantization of a mechanics with infinitely reducible first class constraints. Following an earlier recipe [Phys. Lett. B $381,$ 105 (1996)], the original phase space is extended by purely auxiliary variables, the constraint set in the enlarged space being the first stage of reducibility. The BRST charge involving only a finite number of ghost variables is explicitly constructed.