The core of an assignment market is the translation, by the vector of minimum core payoffs, of the core of another better positioned market, the matrix of which has the properties of being dominant diagonal and doubly dominant diagonal. This new matrix is defined as the canonical form of the original assignment situation. Some well- known core-selections, the tau-value, the kernel and the nucleolus of the assignment game, are proved to be the translation of the kernel and the nucleolus of the canonical representative by the vector of minimal core payoffs.