No.
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South Korea are a Major non-NATO (MNNA) ally. The MNNA status was created in 1989 when the Nunn Amendment, was added to Title 10 (Armed Forces) of the United States Code by Congress. Here it stipulates that cooperative research and development agreements could be enacted with non-NATO allies by the Secretary of Defense with the concurrence of the Secretary of State. Initial Members of the MNNAs were Australia, Egypt, Israel, Japan, and South Korea.