Mini dsplay port to DVI

Hello
Is it possible to display a mac book air on a monitor with a input for DVI?
I am currently using a adpater from mini to HDMI - and then HDMI - DVI cabel. It is probably a problem with my mac book air laptop, but I need to be sure.
Should it work?

Why not just buy one single adapter?

https://www.amazon.com/Apple-Mini-D...sr=1-3&keywords=apple+mini+displayport+to+dvi

Oh great. I where in stores but coulden´t find them. I will order over the internet!