Prince Harry and Prince William Chat as They Leave Grandfather Prince Philip's Funeral Together

Prince Harry and Prince William left their grandfather Prince Philip's funeral together.

The brothers were seen chatting alongside William's wife Kate Middleton as they exited St. George's Chapel in Windsor Castle following the funeral service on Saturday. William, 38, and Harry, 36, continued speaking as they walked away from the church, as Kate stepped away to talk with Sophie, Countess of Wessex.

ITV journalist Tom Bradby, who is friends with the brothers, said, "It is often said that funerals are moments of reconciliation and that is a sight that, to be honest, that many people really wanted to see. Not least those in the family themselves."

Listen below to the episode of our daily podcast PEOPLE Every Day for more on Prince Philip's funeral.

Harry and William joined other members of the royal family, including their father, Prince Charles, in walking behind the Duke of Edinburgh's coffin during the procession to St. George's Chapel.

Instead of being positioned next to each other, their cousin, Peter Phillips (the son of Princess Anne), walked between them.

BBC Kate Middleton, Prince Harry and Prince William

For the procession into the ceremony, William walked with Peter while Harry was behind his brother next to David Armstrong-Jones, the son of Princess Margaret and Antony Armstrong-Jones.

BBC Kate Middleton, Prince Harry and Prince William

RELATED: Prince Harry and Prince William Reunite at Grandfather Prince Philip's Funeral

BBC Kate Middleton, Prince Harry and Prince William

The procession order was "a practical change rather than sending a signal," a Buckingham Palace spokesman said ahead of the service. "This is a funeral and we are not going to be drawn into perceptions of drama. The arrangements have been agreed and represent Her Majesty's wishes."

Samir Hussein - Pool/Wireimage Prince William, Peter Phillips and Prince Harry

This was the first time Prince William and Prince Harry have been together in more than a year, since Harry relocated to California with wife Meghan Markle and their son, Archie. Harry returned to the U.K. last weekend to quarantine at Frogmore Cottage and attend his grandfather's funeral.

Meghan — who is expecting their second child, a baby girl — did not accompany her husband. She "has been advised by her physician not to travel," a royal spokesman said. The Duchess of Sussex watched the funeral from her home in Montecito.

Joe Pugliese/Harpo Productions Prince Harry, Meghan Markle and Oprah Winfrey

In the wake of Meghan and Harry's interview with Oprah Winfrey last month, there are ongoing tensions within the family.

During the tell-all interview on CBS, Meghan refuted reports that she made Kate Middleton cry in the lead-up to her 2018 wedding, saying "the reverse happened." (A source told PEOPLE that both women were in tears over the incident.)

They also accused the royal family of racism — including "concerns" over their children's skin color — and not getting Meghan help when she felt suicidal.

William hit back at the racism claims, telling a reporter during an outing, "We are very much not a racist family."

When asked if he had spoken to Harry after the Oprah interview, he added, "No, I haven't spoken to him yet, but I will do."

Gareth Fuller/WPA Pool/Getty Images Prince William and Prince Harry

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Gayle King, who is friends with Oprah and the Duchess of Sussex, revealed that Harry spoke with William and Charles last month. "The word I was given was that those conversations were not productive. But they are glad that they have at least started a conversation," she said.