The phrase "of their desire" is grammatically correct and can be used in written English.
For example, you could use the sentence "They acted on the basis of their desire for revenge."
"Davenen" had grown out of their desire to "jump around and do something fun to klezmer music," Mr. Wolken said.
America is the image of their desire.
"We're aware of their desire to build ever-taller buildings".
He knows of their desire for a more active response by the government in exile.
Producers and consumers alike speak of their desire for stable oil prices.
But the Saudis have made no secret of their desire for regime change in Syria.
The object of their desire is an obscure Miami-based company, the American Bankers Insurance Group.
"It's not that I don't doubt the sincerity of their desire to protect the talent.
Women voted in a mock election as a demonstration of their desire to gain the vote.
He spoke briefly of his gratitude toward the American people and of their desire for change.
I am convinced of their desire to implement the pause," Kerry said.
