  We study relativistic corrections in exclusive $S$-wave charmonium decays
into proton-antiproton final state. We calculate the NRQCD corrections to the
dominant decay amplitude, which depend on the nucleon twist-3 light-cone
distribution amplitudes only. It is shown that in this case the collinear
factorisation is also valid beyond the leading-order approximation. Our
numerical estimates show that relativistic correction of relative order $v^2$
provides large numerical impact.
