Provided is a method of inducing transdifferentiation of mesenchymal stem cells (MSC), the method including (a) culturing MSC in a first culture medium including a growth factor selected for allowing formation of neuralized MSC (NMSC); (b) allowing the NMSC to proliferate for a sufficient time during which said culture medium is renewed at least once; and (c) culturing the NMSC of (b) in a second culture media including cerebrospinal fluid (CSF) for a time sufficient for the NMSC to differentiate into a population of cells including terminally differentiated neurons, astrocytes and oligodendrocytes. Also provided by the present invention is the use of MSC or NMSC for providing a composition including said population and to kits including MSC or NMSC and instructions for use of same.