Let A be a finite subset of ℤ². We say A tiles ℤ² with the translation set C, if any integer z∈ℤ² can be represented as z₁+z₂, z₁∈ A, z₂∈ C in an unique way. In this case we call A a ℤ²-tile and write A ⊕ C = ℤ². A tile A is said to be a normal ℤ²-tile if there exists a periodic set C such that A ⊕ C = ℤ². We characterize all normal ℤ²-tiles with prime cardinality.