The expressions for the singular parts of the non-adiabatic matrix elements H_ss'(k,R) and Q_ss'(k,R) connecting the states mod ks) and mod ks') of the continuous spectrum of the two-centre problem are obtained. The numerical calculations are performed for the sets of quantum numbers q=0, 1, ..., 7 and m=0 in the interval of values k=0.2(0.1)1.0(0.2)2(1)10 and R=0.1(0.1)20. The asymptotic behaviour of the matrix elements is found as R to 0 and R to infinity .