Improving fingerprint matching algorithms is an active and important research area in fingerprint recognition. Algorithms based on minutia triplets, an important matcher family, present some drawbacks that impact their accuracy, such as dependency to the order of minutiae in the feature, insensitivity to the reflection of minutiae triplets, and insensitivity to the directions of the minutiae relative to the sides of the triangle. To alleviate these drawbacks, we introduce in this paper a novel fingerprint matching algorithm, named M3gl. This algorithm contains three components: a new feature representation containing clockwise-arranged minutiae without a central minutia, a new similarity measure that shifts the triplets to find the best minutiae correspondence, and a global matching procedure that selects the alignment by maximizing the amount of global matching minutiae. To make M3gl faster, it includes some optimizations to discard non-matching minutia triplets without comparing the whole representation. In comparison with six verification algorithms, M3gl achieves the highest accuracy in the lowest matching time, using FVC2002 and FVC2004 databases.