Prince William's wife Kate, the Duchess of Cambridge, was discharged from a London hospital after being treated for acute morning sickness related to her recently announced pregnancy, and has arrived at Kensington Palace.

The royal couple left the hospital Thursday morning, said CBC's Dominic Valitis from London.

The couple's office said she'll be at Kensington Palace for a period of rest.

Kate had been scheduled to attend a couple of charity events this week and on the weekend, but now only William will be going, Valitis said.

The duchess told reporters Thursday she was feeling "much better" as she left the hospital with William, according to U.K. media reports.

She was carrying yellow flowers and the two stopped briefly for photographers before getting in their car.

During her four-day stay in hospital, Prince William visited his wife every day.

"Their Royal Highnesses would like to thank the staff at the hospital for the care and treatment the Duchess has received," Hannah Armstrong said in a statement.

Royal baby would be 3rd in line for throne

Royal officials have said Kate is less than 12 weeks into her pregnancy with the couple's first child.

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The royal couple leaves the hospital on Thursday where Kate, Duchess of Cambridge, was admitted with severe morning sickness early into her pregnancy. (Alastair Grant/Associated Press)

Officials announced the pregnancy Monday, the same day Kate was admitted to hospital. At the time, officials said she was expected to remain there for several days and would require "a period of rest thereafter." 

The couple wed in April 2011 at Westminster Abbey in London.

The child would be third in line to the throne, after Prince Charles and his son William.

Under an agreement to end gender discrimination reached by the Commonwealth heads of state in October 2011, girls would no longer be placed behind a younger son in the line of succession. Plans are in the works to amend the laws governing line of succession.

With files from The Associated Press