We present a non-linear age-structured discrete time population model of semelparous species. A species is called semelparous if it reproduces only once in the lifetime, and usually dies afterwards. We consider only species with lifespan of fixed length. If the life of an organism lasts for n units, e.g. years, the model is given by a transformation on n-dimensional space. We show some amazing properties of the model. We prove that the unique positive stationary point is always unstable if n is even. It seems that the competition between age classes results in the extinction of individuals at all but one age. Therefore, at least locally, the long-time behaviour of the population depends only on an one-dimensional transformation connected with the evolution of the only one persisting age class. We also give some remarks on the continuous-time version of the model.