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Recently, utility grids have emerged as a new model of service provisioning in heterogeneous distributed systems. In this model, users negotiate with providers on their required Quality of Service and on the corresponding price to reach a Service Level Agreement. One of the most challenging problems in utility grids is workflow scheduling, i.e., the problem of satisfying users' QoS as well as minimizing the cost of workflow execution. In this paper, we propose a new QoS-based workflow scheduling algorithm based on a novel concept called Partial Critical Path. This algorithm recursively schedules the critical path ending at a recently scheduled node. The proposed algorithm tries to minimize the cost of workflow execution while meeting a user-defined deadline. The simulation results show that the performance of our algorithm is very promising.