The present invention relates to a new type of concrete safety barrier that is executed in situ, which is a barrier with an asymmetrical configuration with respect to a cross section, i.e., of those called double-profile barriers, which is used as a safety feature on roads and highways hosting road traffic, although it can be used as a guarding or delimiting feature for other activities. This barrier, compared to others known in this industrial sector, is characterised in that it is configured to be able to be executed in situ on a safety dwarf wall already arranged on the road, so it is not required, when executing the barrier, having to first remove the existing dwarf wall to subsequently execute a barrier again.