Can you use an old fitted sheet to turn a new flat sheet into a fitted one?

My favorites (Alexander Julian Watercolors) are long discontinued. One of the fitted sheets just tore. I can find a new flat one of the same color. Can I use the old sheet somehow to turn the new one into a fitted sheet?

I love to mix the colors, seasonally, by mood, or whatever. Right now it’s brown on the bottom, orange on top, and four pillowcases: brown, orange, deep red, and deep green: autumn.

I’d hate to lose the brown out of that mix.

I do have a sewing machine, although I’m a bit rusty with it. The machine is just fine.