Computational Grids are emerging as new infrastructure for Internet-based parallel and distributed computing. They enable the sharing, exchange, discovery, and aggregation of resources distributed across multiple administrative domains, organizations and enterprises. To accomplish this, Grids need infrastructure that supports various services: security, uniform access, resource management, scheduling, application composition, computational economy, and accountability. Many Grid projects have developed technologies that provide many of these services with an exception of accountability. To overcome this limitation, we propose a new infrastructure called Grid Bank that provides services for accounting. This paper presents requirements of Grid accountability and different models within which it can operate and proposes Grid Bank Services Architecture that meets them. The paper highlights implementation issues with detailed discussion on format for various records/database that the GridBank need to maintain. It also presents protocols for interaction between GridBank and various components within Grid computing environments.