In this paper, a pseudo Bayesian argument due to Basu (1971) is employed to construct an estimator for a class of parametric functions namely the population counterpart of a one sample U-statistic of order 2. This estimator is, then, shown to be admissible using a technique given by Meeden and Ghosh (1983). Some admissibility results given by Ghosh and Meeden (1983) and Mazloum (1988, 1990) are shown to be special cases of the admissibility result obtained in this paper.