Wiki: Article VI, Clause 2 of the United States Constitution, known as the Supremacy Clause, establishes the U.S. Constitution, U.S. Treaties, and laws made pursuant to the U.S. Constitution, shall be "the supreme law of the land."
It can't be contrary to the nature or intent of the Constitution, and it's subject to amendment or repeal by Congress.
There's also serious doubt that it is subject to UN treaty law, which was adopted as a part of another treaty. Such layered fiascos send lawyers into leg-kicking bliss like a splayed dog, but have little connection with the original Constitution.
On the other hand, most of what passes for American law these days has little to do with the original Constitution.
As Franklin remarked about our system: "It's a Republic - IF you can keep it.