The article characterizes the factors that cause new challenges for higher education institutions. It is substantiated that in the conditions of intense competition, the best opportunities for further development will be given to the higher education institutions, which will improve their attractiveness to applicants and on this basis will provide the necessary amount of student recruitment. Branding is an effective instrument for forming the attractiveness of a higher education institution. The results of the carried out analysis of the national branding practice indicate that the brand of most higher education institutions is formed under the influence of the history of their development and traditions, industry affiliation and poorly reflects the conceptual features of educational products and the conception of training specialists. In order to adapt to the new challenges, higher education institutions need to implement rebranding to increase their recognition and to stand out against competitors. To do this, a structural and logical scheme of the stages of the rebranding process is proposed, also a methodical approach is developed, expressed in the point-scoring assessment of components of the brand, and the instrumentarium of decision-making for each of them. As a result of successful rebranding, the image of the higher education institution and its attractiveness for applicants will improve, which will increase its competitive advantages, allowing to solve the complex problems associated with increasing the number of students.