Puzzle n°45 (*) - One cat = two fishes

My son wanted to make up a wooden puzzle he could offer as a Christmas present.
Since his mastery of the saw was limited to straight cuts, he designed a very stylised cat, as shown below, only with square shapes.
I added an eye to help imagine the animal...

Now, the challenge consists in transforming this cat into a jigsaw puzzle, with only two pieces which must be of exactly the same shape and dimensions. Are you able to draw the border between the two pieces ?

Clue : the cat will then change into two "fishes" (just as stylised as the cat is !)...

... I'm giving up ...