A general description in the form of an iterative procedure of methods implementing the Single Transferable Vote (STV) is given. Woodall’s axiomatics for ordinal proportional representation systems is examined. New axioms for STV are constructed with modification of quota. The new definition of quota improves the theoretical properties of the procedure. A new method is proposed based on STV and the new definition of the quota. A theorem is proved that this method is the only one satisfying these axioms. This method called the weighted inclusive Gregory method with modified quota and random equiprobable choice of the winning coalition on each iteration. Results are extended to the methods that transfer a fractional number of votes.