Data exchange, in which two blocks of data are swapped between cores in distributed memory systems, necessitates additional memory buffer in a multiprocessor system-on-chip. In this paper, we propose a novel bidirectional inter-core communication mechanism called coherent direct memory access (CoDMA). The CoDMA ensures that the writing address is always less than the reading address in coherent read and write mode, so as to avoid read-after-write (RAW) errors. It features an efficient data exchanging scheme without using data buffer in the memory. A four-core single-instruction multiple-data processor is established for the experiments, based on a multi-bus network-on-chip. Experimental results show that the proposed method consumes no additional memory buffer and achieves 39% and 20% average performance improvement compared with traditional Methods 1 and 2, respectively. And a maximal of 43% reduction in memory usage is achieved, at the cost of only 0.22% more area overhead compared with the entire system.