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The contribution of the center-of-mass (CM) fluctuation of a liquid cluster to the Helmholtz free energy was first discussed by Reiss, Katz, and Cohen (RKC). They argued that this contribution can be assessed via the free energy difference between the cluster with a fixed boundary centered on a fixed CM, and the cluster in which the CM was allowed to fluctuate. They estimated the free energy difference is to be about 20 kbT. Here kb is the Boltzmann constant and T is the temperature of the system. To examine this estimate, Abraham et al. later calculated the Helmholtz free energy of the Lennard-Jones (LJ) cluster with the fluctuating CM via a liquid-state perturbation theory. When compared with that determined by a Monte Carlo (MC) simulation for the LJ cluster with fixed CM, Abraham et al. found a free energy difference is within 7kbT, which is much smaller than 20kbT estimated by RKC. The conclusion of Abraham et al. was then the CM fluctuation of the cluster makes only a small contribution to total Helmholtz free energy. In this note, we report results obtained via MC, for the Helmholtz free energy of the LJ cluster with a fluctuating CM as well as with those for which the CM is fixed. These results are then used to compare with previous theoretical estimate.