Context: Recent results suggest that there is a group of trans-Neptunian objects (TNOs) (2003 EL{61} being the biggest member), with surfaces composed of almost pure water ice and with very similar orbital elements. These objects provide exciting laboratories for the study of the processes that prevent the formation of an evolved mantle of organics on the surfaces of the bodies in the trans-Neptunian belt (TNb). Aims: We study the surface composition of another TNO that moves in a similar orbit, (145453) 2005 RR{43}, and compare it with the surface composition of the other members of the group. Methods: We report visible and near-infrared spectra in the 0.53-2.4 μm spectral range, obtained with the 4.2 m William Herschel Telescope and the 3.58 m Telescopio Nazionale Galileo at the “Roque de los Muchachos” Observatory (La Palma, Spain). Scattering models are used to derive information about its surface composition. We also measure the depth D of the water ice absorption bands and compare with those of the other members of the group. Results: The spectrum of 2005 RR{43} is neutral in color in the visible and dominated by very deep water ice absorption bands in the near infrared (D= 70.3 ± 2.1% and 82.8 ± 4.9% at 1.5 μm and 2.0 μm respectively). It is very similar to the spectrum of the group of TNOs already mentioned. All of them present much deeper water ice absorption bands (D >40 %) than any other TNO except Charon. Scattering models show that its surface is covered by water ice, a significant fraction in crystalline state with no trace (5% upper limit) of complex organics. Possible scenarios to explain the existence of this population of TNOs are discussed: a giant collision, an originally carbon depleted composition, or a common process of continuous resurfacing. Conclusions: 2005 RR{43} is member of a group, may be a population, of TNOs clustered in the space of orbital parameters that show abundant water ice and no signs of complex organics and which origin needs to be further investigated. The lack of complex organics in their surfaces suggests a significant smaller fraction of carbonaceous volatiles like CH4 in this population than in “normal” TNOs. A carbon depleted population of TNOs could be the origin of the population of carbon depleted Jupiter family comets already noticed by A'Hearn et al. (1995).