"on a different direction" is a perfectly correct and usable phrase in written English
It is used to indicate that something (an argument, narrative etc.) is going in a different direction, or taking a different form, to what was previously discussed. For example: "I agree with his argument, but I think we need to head off in a different direction for our discussion".
They certainly decided on a different direction with Fomenko.
Sacks joined Zenefits in December 2014, and since taking over as CEO has promptly started clearing house in order to set the company on a different direction.
On a different direction, there has been shown that correlations exist between Google Trends data and prescription drugs issuing [20, 21] and revenues [22].
Maybe you've had that feeling in your gut -- a sense of apprehension and the need for some clear markers that tell you how to evaluate your relationship and whether to go on or move on in a different direction.
He decided to move on and go a different direction.
Musically, the songs on the album took a different direction from her previous endeavours, incorporating classical music in order to engage an older audience who had been skeptical of her music.
Musically, the songs on this album took a different direction from her previous albums with her former band the Sugarcubes, with the backing music ranging from house, jazz and trip hop styles.
"The legend has it that you look at the flag on the 11th green to determine what the wind is doing on 12. That's great in concept, but reality hits when the flag is blowing one way on 11 and you can feel it in your face from a different direction on the 12th tee.
But one diner took things in a different direction while speaking live on Trump's favorite morning show. .
"I met Marwan on Friday morning and he was very keen to go in a different direction on the coaching front.
"Our strategy has gone in a different direction on the weekends," he said.
