This article is considered to be the first to deal with the problem of outlier-detection in multivariate circular data. The proposed algorithm is an extension of the Local Outlier Factor (LOF) method. Two different circular distances are used; taking into account the close bounded range of circular variables, and testing all possible permutations. The performance of the algorithm is investigated via an extensive simulation study. The performance of the LOF algorithm has a direct relationship with concentration parameter, while it has an inverse relationship with the sample size. For illustrative purposes, the algorithm has been implemented on two medical multivariate circular data, namely, X-ray beam projectors data and eye data. The extension of the LOF algorithm for other types of directional data such as spherical and cylindrical datasets is worth to be investigated.
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