Physical-layer security is usually ensured by the injection of artificial noise (AN) at the legitimate source or destination when relays are cooperative but untrusted. In this work, in order to avoid the power-consuming AN at the legitimate user pairs, the authors investigate multi-pair two-way relaying as a solution for secure transmission in wireless relay networks with untrusted relays. They formulate a generalised problem for the joint design of cooperative beamforming (CB) and AN at relays to maximise the secrecy sum-rate in wireless networks with multi-pair legal users, multiple untrusted relays as well as multiple non-colluding eavesdroppers. Further, they reformulate, approximate and relax the original non-convex problem into a sequence of convex sub-problems based on semi-definite relaxation (SDR) and Taylor series approximation. Particularly, for the reformulated problem they prove that the SDR is in fact tight, and hence propose an iterative algorithm for CB and AN design at the relays. In the simulations, they demonstrate the fast convergence and high achievable secrecy sum-rate of the proposed algorithm. Also, they simulate and discuss the impact of the number of user pairs on the secrecy sum-rate, and reveal the change of performance gain with the number of multiple user pairs.