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outdo  (outdoes 3rd person present) (outdoing present participle) (outdid past tense) (outdone past participle )
1  verb If you outdo someone, you are a lot more successful than they are at a particular activity. 
Both sides have tried to outdo each other to show how tough they can be.  V n 
2 You use not to be outdone to introduce an action which someone takes in response to a previous action. 
not to be outdone  phrase 
She wore a lovely tiara but the groom, not to be outdone, had on a very smart embroidered waistcoat.