In our previous work [8] we defined complex transactions as the combination in any form of aggregate and optional transactions. The solution from [8] proposes an e-commerce protocol for complex transactions in that the customer wants to buy several different physical products from different merchants ensuring strong fair exchange, atomicity, effectiveness, timeliness, non-repudiation, integrity and confidentiality. In this paper, we improve the protocol for complex transactions from [8] by providing a more efficient protocol for each subtransaction from complex transaction. Also, we formally verify our improved solution using AVISPA. The verification results obtained using AVISPA demonstrate that our improved solution preserves all security requirements obtained in [8].