Disc accreting neutron stars come in two distinct varieties, atolls and Z sources, named after their differently shaped tracks on a colour-colour diagram as the source luminosity changes. Here we present analysis of three transient atoll sources showing that there is an additional branch in the colour-colour diagram of atoll sources which appears at very low luminosities. This new branch connects to the top of previously known C-shaped (atoll) path, forming a horizontal track where the average source flux decrease from right to left. This turns the C-shape into a Z. Thus both atolls and Z sources share the same topology on the colour-colour diagram, and evolve in similar way as a function of increasing averaged mass accretion rate. This strongly favours models in which the underlying geometry of these sources changes in similar ways. A possible scenario is one where the truncated disc approaches the neutron star when the accretion rate increases, but that in the atolls the disc is truncated by evaporation (similarly to black holes) whereas in the Z sources it is truncated by the magnetic field.