Context. Shock waves in the solar corona are associated with solar flares and coronal mass ejections (CMEs). Type II solar bursts are radio signatures of shock waves in the solar corona. They are driven by solar flares or CMEs. Despite extensive studies, the intricate spectral patterns observed in type II solar bursts occasionally pose new challenges for the theory of electron acceleration in shocks. Aims. We study a newly identified feature in type II solar bursts called spectral cleaving. This feature is characterized by the actual branching of a type II radio emission lane in radio spectral data. Methods. We analyzed the type II burst exhibiting spectral cleaving in high-fidelity dynamic spectra obtained using the URAN-2 radio telescope (8.25–33 MHz; Poltava region, Ukraine) on 2011 February 14. The high-resolution spectrograms were examined to ascertain its spectral morphology. Results. Our research represents the first recognition of spectral cleaving as a peculiarity of type II bursts that is yet to be classified. This effect occurs due to the shift (or migration) of radio source(s) along a shock front, which in turn is caused by changes in the magnetic field orientation ahead of the propagating shock front. Conclusions. The spectral cleaving observed in solar type II bursts reveals a distinct phenomenon that indicates complex interactions between shock waves and magnetic fields in the solar corona. This discovery enhances our understanding of the mechanisms behind solar radio emissions and emphasizes the need for further observational studies to verify these findings.