If both partners have been tested for HIV and STDs, being in a monogamous relationship creates a protected environment for two HIV-negative and STD-negative individuals to have unprotected sex without worrying about infection.
There are a couple of things to know before settling into this scenario. First off, make sure that you have both tested for HIV and the other STDs and have closed your window period (waited 3 months since you and your partner's last sexual encounter). Taking the condoms off too early can put you and/or your partner at risk for infection if you haven't gotten an accurate test. HIV is easier to give to your sex partner when you are newly infected, and this is often during the period of time when someone can have a negative HIV test, but be HIV-positive.
Being in a relationship can mean many different things to many different people. Does monogamy mean not having any type of sex (whether anal, vaginal or oral) with someone outside of your relationship? Or does it mean not having anal sex outside of your relationship? Or does it mean just not telling if someone makes a mistake and steps outside of the relationship? Life is not often clean cut and fessing up to infidelity is a hard thing to do.
Be sure you are with someone you can trust. HIV is a life-long, life-changing, incurable (and expensive!) infection. Don't be a victim of premature "couple-ation".
Keep life simple, stay negative!