Is it wrong? No. Absolutely not. However, the fact that you're even questioning whether you should leads me to believe that it might not be the best idea. Does your boyfriend know about this chap in basic training that you intend to write a letter to?

Do you hang out with this friend when he's home and the boyfriend doesn't mind?

Even better, what are you doing writing ACTUAL letters to other men anyway when you have a boyfriend. Do you know how personal a written letter is nowadays? In a day of 140 character statements, emails, and texts, taking the time to physically write to somebody is pretty major. Sure when Benjamin Franklin was doing it that's the only way he could keep his women happy. But nowadays, when I get written letters from people, I tend to think thaty they feel pretty doggone strongly for me.

Now I am assuming that when you say write you mean a physical piece of mail. You could mean sending him emails. And once again the question remains - is this somebody that your boyfriend knows about and is comfortable with? Better yet, what exactly won't your boyfriend understand?

From the outside it looks like this: Girl has boyfriend. But girl corresponds with another man whose away on military training via carrier pigeon and written word. Boyfriend would be uncomfortable if he knew, but he doesn't. Girl doesn't think boyfriend should be, he just doesn't understand that its a friend.

So here's the test: if your boyfriend had a friend who had boobs that he was writing to that you found out about, would you be upset? If so, why? If you can honestly say that you wouldn't, then perhaps you are in the clear because you truly believe in innocence and unicorns. But if you know that you'd have an issue with it, then perhaps you should write that letter to your boyfriend instead.