I became friends with my ex's new partner

Girls, I'm literally in shock. Last week, I started a course and I got along really well with a girl there, but yesterday I found out that she is the new girlfriend of a guy I broke up with two years ago and still haven't completely forgotten. The girl has no idea about it, she behaves very sincerely towards me, but I feel strange every time I see her. Do you think I should continue this friendship or should I find an excuse to distance myself? Honestly, it doesn't feel very ethical, but it also seems unfair to the girl. What would you do?