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In any blockchain network, a consensus algorithm is considered a major factor in determining the performance of the network. This study aims to investigate consensus algorithms in healthcare blockchains for electronic health record (EHR) sharing by analyzing the scalability performance of these algorithms. Several consensus algorithms have been proposed in the literature and have been used for various types of blockchain networks. Herein, we analyze the performance of proof of work, practical Byzantine fault tolerance, and proof of authority (PoA) algorithms in the healthcare domain and propose an improved real-time PoA consensus algorithm for EHR sharing for faster consensus and block generation. Results of performed simulations show that the proposed algorithm outperforms previous consensus algorithms in terms of consensus time, number of blocks generated, network throughput, and scalability.