When more repeated measurements than independent observations are available the classical Growth Curve model cannot produce maximum likelihood estimators. In this article we are interested in the estimation of the mean parameters whereas the dispersion parameters are considered to be nuisance parameters. It is possible to produce an unbiased estimator of the mean parameters which is a function of the Moore-Penrose generalized inverse of a singular Wishart matrix. However, its dispersion seems very hard to derive. Therefore, upper and lower bounds of the dispersion are derived. Based on the bounds a general conclusion is that the proposed estimator will work better when the number of repeated measurements is much larger than the number of independent observations than when the number of repeated measurements and the number of independent observations are of similar size.