The Union Jack should be in a "superior position" to the Welsh flag when displayed on government buildings, according to the UK government.
It further clarifies guidance released earlier this week, which said all UK government buildings in Wales should display the flag all year round.
At that time, UK Government Secretary of State for Digital, Culture, Media and Sport, Oliver Dowden said: "The Union flag unites us as a nation and people rightly expect it to be flown above UK Government buildings.
"This guidance will ensure that happens every day, unless another flag is being flown, as a proud reminder of our history and the ties that bind us."
At the same time as announcing the new guidance, which will be brought in over the summer, the UK Government also cut red tape to allow dual flagging - where two flags can be flown on a single pole - for example by flying the Welsh dragon flag alongside the Union Jack.
In a written statement on March 24, Mr Dowden said: "This will allow organisations to highlight local and national identities, for example by flying a Middlesex county flag alongside the Union flag in Middlesex, or the Saltire alongside the Union flag in Scotland.
"Where organisations have two flag poles, they can fly the Union flag alongside another flag, for example flying the Saltire alongside the Union flag in Scotland.
"The Union Flag must always be flown in the superior position."
He added that following the UK's departure from the European Union, express consent must be sought before an EU flag is displayed on a public building in England.
The move follows a row over BBC Breakfast presenters Naga Munchetty and Charlie Stayt, who were accused by some of being "anti-patriotic" after making a joke about the size of the Union Jack on display in Housing Secretary Robert Jenrick's office during an interview with him.
The flying of national flags, including the Union flag, is deregulated in England, Wales and Scotland.
