Armstrong wrote out the sentence, "That's one small step for a man, one giant leap for mankind," before blasting off from Cape Canaveral, Florida, with Apollo astronauts Buzz Aldrin and Michael Collins in July 1969, his brother now says, according to the transcripts of a documentary recently aired on BBC Two.
Because of a radio communications glitch, millions of people watching on television as Armstrong became the first human being to step onto the surface of the moon never heard him utter the word "a" before man.
Armstrong, who died in August at the age of 82, had always maintained he composed the words after touching down on the moon on July 20, 1969, while he waited to leave the Eagle lunar lander.
But Armstrong's younger brother Dean, speaking in an interview for the documentary, "Neil Armstrong - First Man on the Moon" aired on Sunday, said that was not entirely accurate.
"Dean told me that Neil shared the words with him shortly before he left for the Cape, so maybe a couple weeks before the mission," producer Chris Riley told Reuters.
An Armstrong family spokesman did not reply to a request from Reuters for comment.
"I find the timing of Dean Armstrong's revelation to be curious," said Robert Pearlman, owner and curator of CollectSpace.com, a space history website.
"Why wait until after his brother died? He was interviewed for Neil's authorized biography in 2002 and apparently never mentioned this story, despite Neil giving permission to his family and friends to speak openly," Pearlman said.
Andrew Chaikin, author of "A Man on the Moon," which served as a template for an HBO miniseries produced by Tom Hanks, said Armstrong was asked many times over the years when he came up with the quote and always replied that it was spoken spontaneously.
"He had said that many times publicly before I wrote my book, so I never asked him when he made up the quote," Chaikin said.
In the documentary, Dean Armstrong said he and his brother were up one night shortly before Neil left for Florida playing the board game, Risk, Riley said.
Dean said Neil slipped him a piece of paper with the sentence "One small step for a man, one giant leap for mankind," written out and asked Dean what he thought of it, Riley said.
Dean replied, "Fabulous," a transcript of the documentary shows.
Riley, who was commissioned to produce the documentary after
Armstrong's death, said he doesn't see it as raising any real questions about the astronaut's integrity.
"Anybody making that historic step onto another world as a human being would have appreciated the significance of it, as Neil did, and would have given it some thought beforehand. It wasn't something that just sort of came to him as he headed down the ladder. But I don't think he fully decided what to say until maybe after landing," Riley said.
The documentary, produced in partnership with PBS's NOVA is due to air in the United States later this year.