Matisse and Picasso: an exhibition of artistic frenemies at the National Gallery

He wouldn't even pick up the phone when the Matisse family called to give him the news.

But he eventually painted a series of homages to Matisse, including a picture of an empty studio, betraying his deep sense of loss at the death of one of his most constant artistic companions.

"Nobody ever looked at Matisse's work as thoroughly as I did. And he at mine," Picasso would say, years later.

These works, along with 60 other paintings, sculptures and costumes, will be on display at the National Gallery of Australia next week, in a major new show exploring the artistic relationship between two of Europe's greatest 20th century artists.

The rivalry between them was vital to their individual success, and would change the course of 20th century Western European art.

Matisse and Picasso first met in 1906, and for more than 50 years followed each other's creative achievements.

The works in the exhibition, drawn from collections around the world, includes paintings that will be on display in Australia for the first time.

The show also includes 100-year-old costumes from the Ballets Russes, part of the gallery's own collection and designed by both artists to be worn on stage.

Head of international art Jane Kinsman said while many of the works would be familiar to art lovers, it was a rare opportunity to see them together.

"I think people may come away and understand a little more why Matisse and Picasso were so important," she said, as the works were being unpacked and hung in the newly painted space on Friday.

"They were better in combination than if the other hadn't existed, because it was both a rivalry and an artistic companionship, which actually made them better."

She said it was the first major show examining the relationship between the two since a New York exhibition in 2002.

It showed both artists' early work, from before they met, and later as they began to play off each other, even though their styles were vastly different.

Seeing them together gave the work of each artist a new context.

"I've been thinking about [the exhibition] for years and years, and then you have the practical application which takes some time, but it's lovely to see," she said.

Ms Kinsman said Matisse, the older of the two artists, was initially threatened by Picasso's arrival on the scene, but over the years, the two acknowledged and absorbed each other's work.

"It was a very important relationship where they both benefited, although they both gave each other grief and upset each other and sometimes it was almost a boxing match," Ms Kinsman said.