A turbomachine stator element extends around a longitudinal axis and includes a first stator vane and a second stator vane circumferentially adjacent to the first stator vane. Each of the first and second stator vanes include a platform and a blade extending radially from the platform. The stator element also comprising at least one inter-platform seal, arranged between the platform of the first stator vane and the platform of the second stator vane. The inter-platform seal has a flat support provided with an upper surface on which there extends a fin.