Katy Perry's initial attempt to register a "Left Shark" design with the US Trademark Office has been rejected.
The Left Shark - one of Perry's backing dancers at her Superbowl appearance in February - became a viral hit after appearing to forget its dance moves.
The singer's company applied to trademark the costume to stop people from making money from non-licensed designs.
But the request was denied by trademark examiner David Collier.
There was not enough evidence to suggest people identified Left Shark with a Perry performance, he said.
He wrote that the design "identifies only a particular character; it does not function as a service mark to identify and distinguish applicant's services from those of others and to indicate the source of applicant's services".
Collier also said the drawing submitted did not match the actual Left Shark.
The decision comes after a website was ordered to remove a design for a 3D-printed model of the costume.
Lawyers for Perry contacted Fernando Sosa, who had sold the design via an online directory of blueprints, to say Perry had not consented to the use of the shark, which was being sold through Shapeways.com.
"Your unauthorised display and sale of this product infringes our client's exclusive rights," read the letter, posted on Instagram by Mr Sosa.
Mr Sosa was selling the design for $24.99 (£16). After the item was removed by Shapeways, Mr Sosa submitted the design to a different site, Thingiverse, and offered it free-of-charge.