Let X Pn be an unramified real curve with X(R) ≠ 0. If n ≥ 3 is odd, Huisman [9] conjectured that X is an M-curve and that every branch of X(R) is a pseudo-line. If n ≥ 4 is even, he conjectures that X is a rational normal curve or a twisted form of such a curve. Recently, a family of unramified M-curves in P3 providing counterexamples to the first conjecture was constructed in [11]. In this note we construct another family of counterexamples that are not even M-curves. We remark that the second conjecture follows for generic curves of odd degree from the de Jonquières formula.