Sometimes there has to be conflict. It is all in how you MANAGE the conflict.
If this is related to a romantic relationship, I'd recommend looking up John Gottman's work on marital conflict.
If this is related to other kinds of relationships, I'd recommend doing some reading on conflict in interpersonal communications. For one, you want to encourage a positive communication climate. Be prepared to listen and listen well to what the other person has to say. If the climate starts to turn negative (i.e. insults are being bandied about), point that out. In a productive conflict, there is no need for insults. Watch your tone, and stay calm. Be prepared to walk away from the conversation for a while if you need time to calm down and structure your thoughts, or if the communication climate turns too negative.
Here's a pretty decent link with some tips:
Interpersonal Conflict I'm sure you can find more.