Chorion, owner of children's character Noddy, has rejected the latest takeover proposal by rival Entertainment Rights (ER), home to TV puppet Basil Brush.
Basil Brush's owner has made several approaches for Noddy
The UK company said ER's £43.5m ($79.3m) offer was "not in the best interests" of its shareholders.
ER proposed offering a 50-50 mix of cash and shares, worth 252p per Chorion share, last Wednesday.
Chorion rejected a previous unsolicited approach from ER, which it said undervalued the business, in December.
It was the latest of several approaches by ER over the past three years, none of which previously had resulted in an offer, Chorion said.
ER, which also owns Postman Pat, said last week that there was "a strong commercial case for the aggregation of ER and Chorion's content".
The company pointed to "significant cost and
revenue benefits to be generated from a merger of operations".
Britain's takeover watchdog said in December that ER had until 4 February to announce whether it would make an offer for Chorion.