(CNN) A long-standing Boeing 737 emergency procedure that the pilots of two Max jets employed while attempting to avert fatal crashes is under review by the Federal Aviation Administration, according to the head of a major pilots union.

The basic checklist for handling an issue known as runaway stabilizer trim has remained substantially unchanged since 1967, the earliest days of the 737 jetliner, according to Dennis Tajer of the Allied Pilots Association. He said FAA officials told airline safety officials and pilots unions in April of the review.

Such a review is "uncommon" after an accident, said David Soucie, a former FAA safety inspector who is now a CNN safety analyst. Changing the checklist could require pilots to undergo additional training.

The trim on the horizontal stabilizer, on an aircraft's tail, is one way of controlling how steeply the plane climbs or descends. In addition to manual control, it can be moved by the autopilot and a new feature in the 737 Max that has come under scrutiny from crash investigators, the Maneuvering Characteristics Augmentation System, known MCAS. The checklist is intended to give pilots an emergency method to override automated systems and regain control of the plane.

Asked to comment on the review, an FAA spokesman pointed CNN to the agency's statement on the April 12 meeting, which noted a discussion of "pilot training" and said the format "allowed for an open exchange between all participants." The spokesman referred questions about the checklist's history to Boeing, which did not answer a Friday request for details of when the procedure was last revised.

Tajer said the Allied Pilots Association, which represents 15,000 pilots of American Airlines, was prepared at that meeting to ask the FAA for an expedited review of the checklist. He is concerned that the FAA, in his view, has not taken a sufficiently hands-on approach to regulating Boeing and auditing its work and conclusions.

"I want them to be invasive. I want them to be aggressive. I want them to be obstinate about knowing all of the information," he said. "I want them to be more than trust but verify."

The FAA has repeatedly defended its certification of the Max, which involved -- by law -- work that was delegated to Boeing's employees.

"The FAA's aircraft certification processes are well established and have consistently produced safe aircraft designs," the agency said in a statement. "The 737-Max certification program took five years and involved 110,000 hours of work on the part of FAA personnel, following the FAA's standard certification process."

Tajer said that even if the basic steps do not change, the spartan checklist language could be augmented with instructions such as those contained in Boeing supplemental materials: "It may take two pilots to manually trim the aircraft." "It may require elevator load alleviation in order to manually trim the aircraft."

In the wake of the October Lion Air crash in Indonesia, Boeing issued a bulletin for pilots reinforcing the procedure and revealed to them the presence of the MCAS system. Since the second 737 Max crash, in March in Ethiopia, Boeing has defended the runaway stabilizer trim procedure as sufficient. The two crashes killed 346 people.

"Our analysis determined that a pilot would be able to counteract erroneous system input by using the trim switches on the control wheel, or by following the runaway stabilizer procedure and using manual trim," a Boeing spokesman said in an April statement. The statement added that "the appropriate flight crew response to uncommanded trim, regardless of cause, is contained in existing procedures."

The Indonesian and Ethiopian preliminary reports both say the pilots followed the procedure. Both planes ultimately crashed. The reports do not opine on whether an improved checklist could have proved to be lifesaving, but the Indonesian report does note: "None of the (checklists) performed contained the instruction 'Plan to land at the nearest suitable airport.' "

"The crew performed runaway stabilizer checklist and put the stab trim cutout switch to cutout position and confirmed that the manual trim operation was not working," the preliminary report on the Ethiopian crash reads.

Pilots and experts frequently refer to the runaway stabilizer trim checklist as a "memory item," an emergency procedure that pilots train on repetitively and can perform almost instinctively.

"Those items that are ingrained into your brain come over after hours and hours of simulator training," explained Soucie, the safety analyst, and changes to them could require pilots to perform additional simulator training.

Tajer said FAA officials also disclosed reviews of two other emergency checklists -- for handling inaccuracies known as airspeed and angle of attack -- and that the reviews can help determine if the lists contain the details they need several generations of 737 later.

The procedures have not been updated, he said, "since Lyndon Johnson was President and the country was struggling with the Vietnam War."