We have studied the dynamical evolution of a compact group of four galaxies, using Aarseth's NBODY2 code. An important departure from previous studies is the wider range of masses chosen for the individual galaxies, which are representative of those existing in Hickson's catalog. The first merging occurs after 4.3 x 10(9) yr, while the group lasts for as many as 9 x 10(9) yr before merging into a single remnant. Two other simulations test the dependence of the results on the galaxy models adopted and the general set of initial conditions. Another run, with four identical galaxies and no special initial conditions, is used as a standard of reference. This Letter emphasizes that the use of a significant range of galaxy masses, and the presence of quasi-stable orbits, delays the transfer of orbital energy into internal energy through dynamical friction and tidal stripping, thus prolonging the lifetime of even compact groups.