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The Internet has been encouraging and enabling business collaborations via online transactions over the Web. However, managing transactions in a long-running business process across domains still remains a challenge. In this paper, we propose a novel financial-compensation-based transaction management model, fcBTxM, to address this challenge. Unlike classical transaction management, fcBTxM does not attempt to recover data consistency via rollback when a failure occurs. Instead, our model always tries to forward-roll a business process via financial compensation. We use a state machine to capture and describe the states of our transaction model and their relationships. We also develop a set of technologies and protocols for enabling the new transaction management. A real business collaboration example is used to demonstrate the concept, and preliminary testing results are provided to evaluate our technologies.