I don’t know if I would say that it is normal, but it does happen a lot. It even happens after you have bult up your recall to the level that you normaly recall several dreams a night.
You could look at this topic to get some help with DR.
[Dream Journals - The more you use them, the better!)
It is about dream journals, but has some tips on DR. If you search for dream recall, you will also find lots of posts here.
don