Fatou's example

Examples due to P. Fatou and L. Biberbach show that Picard's little theorem cannot be extended to apply to holomorphic mappings of the complex space $C^n$, $n>1$. These examples are used to construct a pair of functionally independent entire functions of two complex variables such that the image of $C^2$ by the mapping realized by this pair does not contain any sphere. Here we give an example of the same type which implies a stronger assertion concerning the set of values not taken.