Story highlights Adm. Brian Losey writes an open letter to Navy SEALs on October 31

The letter came just days before a "60 Minutes" appearance by Matt Bissonnette

Bissonnette said he was on the Pakistan raid in which Osama bin Laden was killed

Losey reminds SEALs they've made a vow to maintain mission secrecy and eschew glory

The head of Naval Warfare Special Command had warned Navy SEALs against betraying their promise to maintain secrecy just days ahead of a SEAL's "60 Minutes" interview defending his publication of details from the Osama bin Laden mission

The open letter specifies that the warning holds even after a mission is over, and it scolds those seeking public credit.

The admonition is seemingly directed both at Matt Bissonnette -- who revealed his role on the 2011 bin Laden mission with "60 Minutes" on Sunday -- and at a SEAL at the center of an upcoming Fox News documentary. It was Bissonnette's second interview with the CBS show.

The October 31 letter from Adm. Brian Losey obtained by CNN was addressed to "teammates" and sought to shame those who sought public acclaim, reminding SEALs "the most important credit we can garner is the respect of our Teammates and Partners."

Letter speaks of core values, private accolades

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"We do not abide willful or selfish disregard for our core values in return for public notoriety and financial gain," Losey wrote.

"Any real credit to be rendered is about the incredible focus, commitment, and teamwork of this diverse network and the years of hard work undertaken with little individual public credit. It is the nature of our profession," he also wrote.

The missive was first reported by SOFREP, a website that covers the Special Operations community.

The letter is not the first. Losey's predecessor also sent a letter reminding SEALs to keep the confidence of the mission.

While Losey does not mention the bin Laden raid directly, it's the publication of those details and the mission to free the captured sailors of the Maersk Alabama in 2009 off the coast of Somalia that have gotten much publicity.

SOFREP has identified the so-called "shooter" of bin Laden, who was the unnamed subject of a Esquire magazine article last year and whose identity will reportedly be revealed in an upcoming Fox News documentary. CNN has not confirmed the name of the SEAL is accurate.

The claims in the Esquire article were met with skepticism by those in the SEAL community who said the close quarters and darkness and intense shooting made it difficult to determine whose bullets killed bin Laden

Criminal inquiry into Navy SEAL

The Pentagon and Justice Department are conducting a criminal inquiry of Bissonnette and his bestselling book about the raid in Pakistan. That inquiry has delayed a legal settlement between the government and the author over profits from the book.

Bissonnette didn't seek the legally required government review before he published the book " No Easy Day " in 2012. The book recounts what he says is his role as one of the SEAL Team Six members who shot and killed bin Laden.

The Pentagon will not even confirm that Bissonnette was even on the raid.

Navy Cmdr. Amy Derrick-Frost, a spokeswoman, would only say of Bissonnette and his connection to the mission: "If in fact this individual was associated with the military unit that carried out the UBL raid ... is yet to be determined."

Bissonnette notes that while he revealed details, so did the CIA and Pentagon when they cooperated with the filmmakers of "Zero Dark Thirty," a dramatic retelling of the hunt for the al Qaeda leader.