The Labrouste transforms (Labrouste and Labrouste, 1940) of class $\Pi (s)_{L}$ generate pseudo-harmonic fluctuations of a random process because the results in transformed series are mutually correlated, even in the cases when original series represent a white noise. In the case of the analyzed $\Pi (s)_{L} = (s_{6}s_{8})_{12}$ transform, appropriate for the filtering of the known 50-day oscillation of the length of the day and the atmospheric angular momentum, the amplitude A of the pseudo-harmonic fluctuation does not exceed 5% of the standard deviation $\sigma$ of original data.