The Labrouste transforms of the class $\Pi (T)$ generate pseudo-harmonic fluctuations of a random process because the series of mutually correlated observations \{$Y_{i}$\} are obtained even when the series of white noise \{$X_{i}$\} are transformed. In the case of $\Pi (T) = T_{2}T_{3}T_{3}T_{4}$ transform amplitudes A of pseudo-harmonic fluctuations satisfy the relation: $A/\sqrt{\sigma}$ = c(n), where $\sigma$ is the standard deviation of results in the original series and c(n) is a parameter depending on the number of observations n. When n is increased, c(n) decreases. For example, if n = 500, c(n) = 0.18 and if n = 10000, c(n) = 0.03.