Consistent Batalin--Fradkin quantization of Infinitely Reducible First Class Constraints

We reconsider the problem of 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 first stage of reducibility. The BRST charge involving only a finite number of ghost variables is explicitly constructed.