In resource allocation for secure cooperative communication systems, along with power allocation, relay placement also has equal importance in improving the system performance. In this paper, we study the joint optimization of relay placement and power allocation to minimize the secrecy outage probability (SOP) for a four- node cooperative system with a trusted randomize- and-forward relay in the presence of an external eavesdropper. Initially, we derive the expression of SOP, and then formulate an optimization problem to minimize SOP under given power budget and relay placement (RP) constraints. By providing analytical insights on power allocation (PA) between source and relay, we obtain closed form expressions of optimal PA (OPA) for a given RP that minimizes the SOP. Next, we propose a low complexity algorithm to obtain the near-optimal RP (ORP) for a given PA. Finally, we obtain optimal SOP with joint RP and PA. Numerical results present validation of analytical SOP through Monte Carlo simulations, optimal PA for a given RP, optimal RP for a given PA, and joint PA and RP for a given secrecy threshold rate. Finally, we highlight the significant performance gains achieved by the joint design over the conventional scheme. © 2019 IEEE.