When White House reporters heard that the man who fluffed his lines on Barack Obama's big day, the chief justice, John Roberts, was in the building, they assumed he had come to apologise.

But Roberts had not come to say sorry, though he may have done that too. He was there for what Americans call a do-over, to have a second go at the swearing-in ceremony.

This time Roberts - and Obama - got the words in the right order.

While constitutional experts, as well as the White House's own lawyers, insisted a repeat of Tuesday's ceremony was not necessary, Obama's team is web-savvy and had watched the conspiracy theories building up on the internet. There was a lot of traffic suggesting Obama was not in fact president. A rerun seemed to be the fastest way to try to stop the speculation getting out of control.

In contrast to Tuesday's ceremony, what happened a day later was an extremely low-key affair. Although there were millions who watched in the cold on the Mall on Tuesday, there were less than a dozen in the Map Room to witness the second attempt.

Reporters were only alerted to Roberts's presence when one of them overheard Obama's adviser, David Axelrod, in a conversation in a corridor. Four reporters were invited to witness the second ceremony, along with a photographer. Also present were Axelrod, Robert Gibbs, the White House press secretary, and Greg Craig, the White House counsel.

The president was supposed to say on Tuesday: "I do solemnly swear that I will faithfully execute the office of president of the United States." But Roberts misplaced one word, saying: "I will execute the office of president of the United States faithfully."

Obama told the small group gathered in the White House he had decided to do it again because it had been so much fun the day before. Roberts donned his black robe and asked: "Are you ready to take the oath?" Obama replied: "I am, and we're going to do it very slowly."

He is not the first president to have to repeat the ceremony: Calvin Coolidge and Chester Arthur also had to.

After the rerun, Obama joked with reporters that they were also going to repeat the rest of inauguration day. "The bad news for the [reporters] is there's 12 more balls," he said.

In a statement afterwards, Craig said he believed that the oath had been effectively administered on Tuesday. "But the oath appears in the constitution itself. And out of an abundance of caution, because there was one word out of sequence, chief justice Roberts administered the oath a second time," he said.

That is not likely to end the conspiracy theorists. There is already traffic asking why Obama did not swear on a bible the second time round. Others suggested that, since he was not legally president for much of Wednesday, the executive orders he had signed until that point were not legally binding. Others ask why television cameras were not present.

In reality, Obama did not even have to be sworn in on Tuesday. There is a near-consensus among lawyers and politicians that he became president at noon on Tuesday, and had been for four minutes when he took the oath of office at 12.04pm.