In this paper, a method of allocating operational risk regulatory capital using a closed-form Shapley method, applicable to a large number of business units (BUs), is proposed. It is assumed that if BUs form coalitions, the value added to a coalition by a new entrant is a simple function of the value of that entrant. This function represents the diversification that can be achieved by combining operational risk losses. Two such functions are considered. The calculations account for a service that further reduces the capital payable by BUs. The results derived are applied to recent loss data.