Yes but that isn't a section of the UN Charter as stated by the other poster. Any one of the Big Five have the power to veto the UN Sectretary General appointee and thus it can be expected that one of the five would veto someone from one of the other four but that isn't in concrete.
I'm looking for the section of the UN Charter that prohibits such an appointment which I can't find and no one to this date has been able to provide but the claim stays out there.
I haven't found it either. Going by the excerpts of the articles I'm quoting from, it looks like they have few rules in place and most of their current "rules" are simply going by past procedures with nothing actually set in stone.
United Nations Association of the United States of America (UNA-USA)
Selecting a United Nations Secretary-General: A Context for Reform?
February 2006
Background
Despite these far ranging responsibilities, the UN Charter provides minimal guidance on the process of selecting the UN's top diplomat, stating simply that "the Secretary-General shall be appointed by the General Assembly upon the recommendation of the Security Council."
There are no explicit criteria or qualifications for the post, including term limits or country of origin. In practice, this has given the five permanent members of the Security Council (China, France, Russia, the United Kingdom and the United States) veto power over the selection process within the council since the UN's founding.
The General Assembly has had the theoretical power to override the council's selection by failing to give the recommended candidate the necessary majority vote; nonetheless, to date, the General Assembly has never rejected a candidate referred by the Security Council.
Due to a lack of official guidelines, some precedents have emerged over the years with respect to choosing the secretary-general. The post's tenure lasts either one or two terms of five years. The selection is based on a geographical rotation, and it is generally accepted that the secretary-general should not originate from one of the permanent five member states.
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Viewpoints - Discord Expected Over Kofi Annan's Successor
Proposed Selection Process Changes
Radio Free Europe (Feb. 21) had this to report about the selection process: "there is an unwritten agreement that the secretary-general will not be a national of any of the five veto-holding permanent members of the council — China, France, Russia, Great Britain, and the United States. So far, this informal rule has held. And some U.N. diplomats express regret behind the scenes that because of it, former U.S. President Bill Clinton probably is not eligible to head the world body."
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