It has been noted that, in classical extremely metal-poor (EMP) stars, the abundance ratio of Sr and Ba, is always higher than [Sr/Ba] = -0.5, the value of the solar r-only process; however, a handful of EMP stars have recently been found with a very low Sr/Ba ratio. We try to understand the origin of this anomaly by comparing the abundance pattern of the elements in these stars and in the classical EMP stars. Four stars with very low Sr/Ba ratios were observed and analyzed within LTE approximation through 1D (hydrostatic) model atmosphere, providing homogeneous abundances of nine neutron-capture elements. In CS 22950-173, the only turnoff star of the sample, the Sr/Ba ratio is, in fact, found to be higher than the r-only solar ratio, so the star is discarded. The remaining stars (CS 29493-090, CS 30322-023, HE 305-4520) are cool evolved giants. They do not present a clear carbon enrichment. The abundance patterns of the neutron-capture elements in the three stars are strikingly similar to a theoretical s-process pattern. This pattern could at first be attributed to pollution by a nearby AGB, but none of the stars presents a clear variation in the radial velocity indicating the presence of a companion. The stellar parameters seem to exclude any internal pollution in a TP-AGB phase for at least two of these stars. The possibility that the stars are early-AGB stars polluted during the core He flash does not seem compatible with the theory.