Grid Resource Discovery Service is currently a very important focus of research. We propose a scheme that presents essential characteristics for efficient, self-configuring and fault-tolerant resource discovery and is able to handle dynamic attributes, such as memory capacity. Our approach consists of an overlay network with a hypercube topology connecting the grid nodes and a scalable, fault-tolerant, selfconfiguring search algorithm. By design, the algorithm improves the probability of reaching all working nodes in the system even in the presence of failures (inaccessible, crashed or heavy loaded nodes). We analyze the static resilience of the presented approach, that is to say, how well the algorithm is able to find resources without having to update the routing tables. The results show that the presented approach has a high static resilience. Keywords-static resilience; fault-tolerant; grid resource discovery; hypercube overlay network