Studying the evolution of the morphological distribution of galaxies in different environments can provide important information about the effects of the environment and the physical mechanisms responsible for the morphological transformations. As part of a complete analysis of the young cluster RXJ 1257+4738 at z ~ 0.9, in this work we study the morphological properties of its galaxies. We used non-parametric methods of morphological classification, as implemented in the galSVM code. The classification with the applied method was possible even using ground-based observations, as the r'-band imaging from OSIRIS/GTC. We defined very conservative probability limits, taking into account the probability errors, to obtain a trustworthy classification. In this way we were able to classify ~30% of all cluster members and to separate between late-type (LT) and early-type (ET) galaxies. Additionally, when analysing the colour-magnitude diagram, we observed a significant population of blue ET galaxies among the classified ones. We discussed possible explanations for finding this population. Moreover, we studied different physical properties of LT, ET, and blue ET galaxies. They turn out to be comparable, with the exception of the stellar mass that shows that the red ET population is more massive. We also analysed the morphology-density and morphology-radius relations observing that, only when considering the morphological separation between ET and LT galaxies, a mild classical behaviour is obtained. RXJ 1257+4738 is a young galaxy cluster, showing a clumpy structure, which is still in the process of formation, and which could explain the lack of some of the standard morphological relations. This makes this cluster a very attractive case for obtaining higher resolution data and for studying the morphological properties of the entire cluster in more detail and their relation to the environment. The catalogues are only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (http://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/592/A108