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This paper describes an advanced coordination method for an optimized protection time grading based on a new nonstandard tripping characteristic for overcurrent protection relays. The intention is the highest possible reduction of tripping times for a selective fault clearing in distribution networks protected by overcurrent relays without communication links. The new nonstandard tripping characteristic will be described from its basic idea to its constraints of the optimization problem. The optimization is solved by the method of Lagrange generalized with the Karush-Kuhn-Tucker conditions and is aimed at selective fault tripping with shorter tripping times as standard characteristics and conventional coordination methods. Overcurrent relay coordination becomes a mathematical optimization task. A comparison with the standard characteristics and conventional coordination methods shows a notable advancement regarding their average and maximum tripping times which can be achieved using this new method.