We estimate the three-point correlation function for samples of galaxy clusters identified from the Lick galaxy catalog at different density thresholds in order to test the ability of the biasing prescription to account for the different correlation properties of different hierarchy cosmic structures. We use two methods: the moment method and the direct counting of triplets. Sampling errors are estimated by means of bootstrap procedure. By assuming the hierarchical expression for the connected three-point function, we find that the two methods give consistent estimates of the Q-values, while the associated uncertainties are rather different. In particular, larger errors are always obtained from the moment method. In all the cases, however, our bootstrap resampling errors turn out to be greater than those obtained by other authors, based on Poissonian statistics. For clusters identified at the higher threshold levels of the underlying galaxy field we obtain Q ~ 0.5-0.8. Note, however, that even at the highest overdensity level our clusters are on average poorer than the Abell ones, and this could well be the reason why our Q-values are slightly smaller than those obtained from the Abell catalog. A general trend is found for the Q-values to take smaller values as the height of the threshold decreases. This agrees with the expectation of biasing models, where non-Gaussianity arises as a threshold effect.