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