The present paper investigates the effects of a coupling element placed between nonlinear self-excited oscillators on synchronization. A simple nonlinear model is newly developed by modifying the model treated in our previous report. This model consists of two oscillators subjected to Coulomb friction and a block installed in the coupling element. These elements are connected in series by coil springs and dashpots. In this model, stick-slip motion frequently occurs due to Coulomb friction. The synchronized solutions and the stability are analyzed accurately by the improved shooting method. The new model is validated by comparing the calculated results and the experimental results, and the features of the synchronized solutions are investigated. The results reveal that the frequencies and vibratory patterns closely correspond to the natural frequencies and natural modes of a three-degree-of-freedom system without Coulomb friction and that the existence regions of the synchronized solutions depend on the block mass as a parameter of the coupling element. When the parameter is set appropriately, the existence regions expand. The mechanism behind this is examined from the viewpoint of the energy transition between oscillators.