In this paper, we present an algorithm called redundant logical paths (RLP) for efficient HSR traffic reduction. It creates redundant logical paths between each HSR node and all the other nodes. Eventually, a logical full-meshed network or paths will be established among all HSR node types, except the Quadbox type, which is used only for interconnection. The logical full-meshed network will be used instead of using the standard HSR protocol that depends on the concepts of the duplication and forwarding of the received frame until it reaches the destination node. The RLP algorithm results in significantly less frame traffic because there is no random forwarding as in the standard HSR protocol. For the sample network in this paper simulation results showed a 61.5-80% reduction in network frame traffic compared to the standard HSR. Our algorithm will avoid latency issues in the network and even network congestion, thus improving network efficiency.