  In 1984, H. Yoshihara conjectured that if two plane irreducible curves have
isomorphic complements, they are projectively equivalent, and proved the
conjecture for a special family of unicuspidal curves. Recently, J. Blanc gave
counterexamples of degree 39 to this conjecture, but none of these is
unicuspidal. In this text, we give a new family of counterexamples to the
conjecture, all of them being unicuspidal, of degree 4m + 1 for any m \geq 2.
In particular, we have counterexamples of degree 9, which seems to be the
lowest possible degree.
