We revisit the issue of probing R-violating couplings of supersymmetric theories at hadronic colliders, particularly at the LHC. Concentrating on dimuon production, an evaluation of the optimal sensitivity to the R-violating coupling is performed through a maximum likelihood analysis. The measurement uncertainties are evaluated through a study of fully generated events processed through a fast simulation of the ATLAS detector. It is found that a host of R-violating couplings can be measured to a statistical accuracy of better than 10%, over a significant part of the m_{tilde f} -- lambda parameter space still allowed by low energy measurements. Since the bounds thus obtained do not simply scale as the squark mass, one can do significantly better at the LHC than at the Tevatron. The same analysis can also be extended to assess the reach of the LHC to effects due to any non-SM structure of the four-fermion amplitude, caused by exchanges of new particles with different spins such as leptoquarks and gravitons that are suggested by various theoretical ideas.