Summary: We consider the maximum likelihood estimator (MLE) for the mean direction of the Langevin distribution and derive its asymptotic properties. First, we derive the expectation and the MSE (mean square error) of the MLE in the form of asymptotic expansions. We also consider the estimator so modified as to satisfy higher order asymptotic unbiasedness. Further, it is shown that the MSEs of the MLE and the modified estimator are coincident up to the order \(n^{-1}\).