This study is to suggest new educational concepts such as ``attaching separation``, ``separately ascending education``, and ``cooperatingly ascending education``. These concepts are expected to reveal new types of education relatively unexplained by endogenous theory of education. In most cases, education is conceived to be possible between the more advanced and the less advanced of same kind of transcendental world, and reduce the gap or differences between their transtalents. But education can be actualized between rivals of different sects within same transcendental world, or people possessing equivalent transtalents. This study focused competition and cooperation between Matisse, Picasso, and Braque and showed the various activities and phenomenon related to ascending education. According to the results of this study, education can be re-conceived to deepen and intensify the differences of educational participants`` transtalents, or bring new transtalent to various transcendental worlds by cooperation of participants. Education can be re-conceptualized to be one of important factors to make different sects or schools within a transcendental world or new transcendental world itself.