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Step bunching at a growing crystal surface is usually attributed to the presence of the Ehrlich–Schwoebel (ES) effect caused by the asymmetry of the attachment kinetics at a step. Here, we show that, contrary to the case of rectilinear motion, step bunches at the solid-liquid interface of a nanowire grown by the vapor-liquid-solid process can form even in the absence of the ES effect. It is found that two circular steps propagating from the edge of the nanowire inward form a bunch if the initial distance between the steps is less than a critical value. This effect is caused by the interaction of steps with each other via the diffusion field in the bulk of the liquid catalytic particle. The normal ES effect promotes the bunching, while the anomalous ES effect delays it.