Recent studies have revealed that solar jets involving minifilament eruptions may be initiated under the wellknown magnetic-breakout mechanism. Before or just at the onset of those jets, there should be a current sheet, where breakout magnetic reconnection takes place, between open fields and the outside of the jet-base arcade carrying a minifilament in its core. In this paper we present a jet produced by the eruption of two minifilaments lying at the jet base. A current sheet is directly detected near the jet base before the onset of the eruption, suggesting the magnetic-breakout mechanism. However, we further find that the current sheet undergoes a transition. The current sheet first shortens to zero in length, but then lengthens toward an orthogonal direction relative to its initial orientation. The change of the current sheet gives rise to a reversal of the breakout reconnection, as the inflow and outflow regions before the transition become the outflow and inflow regions after the transition, respectively. We therefore propose that this observation provides evidence for the so-called oscillatory reconnection that is defined by a series of reconnection reversals but not yet proven to exist in the real plasma environment of the solar atmosphere.