Radio environment maps (REMs) have demonstrated their significance in spectrum sensing, control, and sharing, particularly in relation to unmanned systems, the Internet of Things (IoT), and 5G communication. However, they encounter challenges related to meeting the increasing accuracy requirements. This paper introduces the BHM-RK algorithm, a novel approach for constructing REMs in scenarios with multiple transmitters. The algorithm utilizes spatial clustering for transmitter partitioning, Bayesian posterior inference within partitions, and residual Kriging interpolation to address challenges posed by diverse transmitter influences. Experimental validation demonstrates the superior performance of the BHM-RK algorithm in terms of construction accuracy compared to existing methods, highlighting its effectiveness in enhancing precision in REM construction for scenarios with multiple transmitters.