We study the properties of the fossil cluster RX~J1416.4+2315 through g'and i'-band imaging and spectroscopy of 25 member galaxies. The systemis at a mean redshift of 0.137 and has a velocity dispersion of 584 kms$^{-1}$. Superimposed onto one quadrant of the cluster field there isa group of five galaxies at a mean redshift of 0.131, which, if includedas part of the cluster, increases the velocity dispersion to 846 km/s.The central object of RX~J1416.4+2315 is a normal elliptical galaxy, withno cD envelope. The luminosity function of the system, estimated bythe number counts, and statistical background correction, in the range --22.6 $<$ M$_{g^\prime}$ $<$ --16.6, is well fitted by a Schechter functionwith M$_{g^\prime}^* = -21.2 \pm 0.8$ and $\alpha = -1.2 \pm 0.2$ (H$_0$= 70 km s$^{-1}$ Mpc$^{-1}$, $\Omega_M$=0.3, $\Omega_{\Lambda}$=0.7).The luminosity function obtained from the spectroscopically confirmedmembers in both g$^\prime$ and i$^\prime$ bands agrees qualitativelywith the photometric results. The mass of the system RX~J1416.4+2315,$\sim 1.9 \times 10^{14}$ M$_\odot$, its M/L of 445 M\sol/L$_B$\sol ~ and L$_X$ of 22 $\times$ 10$^{43}$ h$^{-2}_{50}$ ergs s$^{-1}$ (bolometric)suggest that this system is the second example of known fossil {\itcluster} (after RX~J1552.2+2013) confirmed in the literature. (AU)