According to the literature innovation is the adoption of an internally generated or purchased device, system, policy, program, process, product or service that is new to the adopting organization. Moreover, based on bibliography and among other data, the adoption of innovation is conceived to encompass the generation, development and implementation of new ideas and behaviors or concerns the selection and initial use by an organization or sub-unit of a practice that had not been used previously. Usually, the adoption process is either a response to changes in the internal and external environment or a preemptive action taken in order to influence that environment. This paper is about a research in relation to the ideas, the possibility and capability of the headteachers in Greek primary schools to reinforce teachers in generating or adopting and implementing innovations. We should not forget that the Greek educational system is considered to be a highly centralized system and that affects seriously the generation, the adoption and the implementation of any innovation. Taking into account the fact that the role of the headteacher, even in centralized educational systems, is, possibly, of the most important administrative roles, we attempted to identify if the Greek head-teachers encourage the educational staff to implement innovation. The research was held by using questionnaires and interviews as methodological tools and a hundred head-teachers of primary schools participated. Methodologically speaking we can not assume that this number represents all the headteachers in the Greek primary education. But we can consider the data of this research as a base for the enrichment of our knowledge and for the designing and implementation of a macro-scaled research in the near future.