The current research in mining length-two loops depends on "aba" pattern. However, the pattern does not necessarily appear in the logs that satisfies local completeness. This research aims at finding ways to mine length-two loops without the pattern. It results in a new algorithm (α^L+-algorithm) that is based on the α-algorithm. First, an order vector matrix is established by tasks in logs to abstract variant structures of length-two loops. Then, distinction between loops and concurrency structure is obtained by event's frequency and location in traces. Finally, proximity and circuit abstraction are used to eliminate the interference caused by the concurrent branches. The experimental results show that the α^L+-algorithm can handle length-two loops with or without "aba" pattern. In addition, the α^L+-algorithm is implemented in the ProM tool.