We study the index coding problem in the unicast message setting, i.e., where each message is requested by one unique receiver. This problem can be modeled by a directed graph. We propose a new scheme called interlinked cycle cover, which exploits interlinked cycles in the directed graph, for designing index codes. This new scheme generalizes the existing clique cover and cycle cover schemes. We prove that for a class of infinitely many digraphs with messages of any length, interlinked cycle cover provides an optimal index code. Furthermore, the index code is linear with linear time encoding complexity.