Direction-of-arrival (DOA) estimation with unfolded co-prime linear arrays has been investigated thanks to the large aperture, excellent performance, and full degrees-of-freedom (DOFs). Besides, it has been admitted that the ambiguity problem can be suppressed thanks to the co-prime property. However, it is not always true. When there are two different DOAs having the same directional vectors with a given DOA for the two subarrays, ambiguities would still be found at the angles of which the corresponding directional vectors can be represented as linear combinations of the directional vectors of true DOAs. Surprisingly, this problem has been ignored by all the existing work. In this letter, this ambiguity problem is discussed for the first time to the best of our knowledge, and an appropriate method for fixing it is proposed. Compared to the original method, the proposed method contains all the advantages of unfolded co-prime linear arrays and can solve the ambiguity problem successfully and efficiently. Numerical simulations are given to show the reliability and performance of the proposed method.