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We point out that for sufficiently strong shocks, with Mach number $ M_1 >\sqrt{\frac{3 \gamma -1}{(3-\gamma ) \gamma }}= 1.34$ ($\gamma=5/3$), thesolutions for cosmic ray-modified shocks experiences a bifurcation. As aresult, for super-critical flows an isothermal jump forms (which is not ashock). The isothermal jump forms due to the energy diffusion of fast, butenergetically subdominant cosmic rays. For super-critical flows the isothermaljump appears regardless of a particular feed-back mechanism from the CRs. Thecompression ratio at the isothermal jump is $2/ (\gamma-1)=3$, so that in thetest particle regime the expected spectrum of low energy CRs experiencingfirst-order Fermi process is $p = 2\gamma/(3- \gamma) = 5/2$, steeper thanconventional $p=2$.

Cosmic ray-modified shocks: appearance of an isothermal jump