Authority to revoke National Monument designations? Not according to this Constitutional scholar.

Passed in 1906 by the US Congress, the US Antiquities Act has allowed presidents of both the Republican and Democratic parties to protect land already in federal control from development and harm by naming national monuments. The current US President has decided that his predecessors have "abused" this power by naming more than 11 million acres of land and 760 million acres of land as national monuments. Hence, the president has ordered the Secretary of the Interior to review monument designations that affected more 100,000 acres since 1996 for possible de-listing.
Since that review was announced, many people have been looking at the Act to determine the limits of Presidential authority regarding previous designations. This constitutional scholar believes any president can designate national monuments, but may not revoke designations made by previous presidents, at least under current law.
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Antiquities Act of 1906: No Presidential License to Revoke National Monuments
By Bruce Fein
Huffington Post
July 30, 2017