By means of the quadratic magnetoelectric effect the components of the non-linear magnetoelectric susceptibility tensor βijk of the antiferromagnetic ferroelectric ferroelastic phase of BiFeO3 have been determined at 4 K: β_111 =5.0·10^-19[sA^-1],β_113=8.1·10^-19[sA^-1], β_311 =0.3·10^-19[sA^-1],β_333=2.1·10^-19[sA^-1]