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In this dissertation, the emotional intelligence (EI) and social intelligence (SI) of school principals is investigated as a factor in improving the relationships of school unit (principals and teachers) members in Primary Education. The purpose of the dissertation is to identify the needs of developing the above variables through the bibliographic and research process so as to make suggestions that would improve the existing situation in teachers’ relations. The work is divided into two parts. Initially, the bibliographic references are introducing us to concepts and definitions related to leadership and education, and then we are led to the recording of concepts of emotional and social intelligence in general and specifically in education. The second part of the paper presents the primary research of the above variables through the views of teachers about their school principals. The views attempt to capture the ESI of school principals where teachers work as well as the leadership style associated with improving relationships and conflict management at school. The methodological approach used is quantitative with the use of a digital questionnaire. The SPSS 23 statistical program is used to derive the results. In conclusion, participants record their views of the principals with relatively high levels of ESI. In addition, in most cases managers seem to operate in a democratic and transformational leadership style as they make particular use of conflict management style in integrating goals and problem solving in a collaborative manner. For these reasons, it is suggested that a holistic approach to improving relationships and conflict management should be provided to all teachers through knowledge and development of their emotional and social intelligence.