There are several things to do to put an end to bickering.
The first answer is to ignore the bicker. If you can stay out of it, completely out of it, the bickering tends to end. Children find better ways to problem solve, they lose interest and move on. If you involve yourself, try to sort things out and take sides you reinforce the bicker. Getting involved adds fuel to the fire.
If you truely can’t ignore the bicker, the second answer is to be the blanket, come down on both. You might say, “wow, this is too loud. I need you both to quiet down,” or, “this is too much. Both of you find another place to play.” Here you are ending the bicker, but without getting involved.
In either case, start spending more time coaching the positive behaviors. Talk to your children about how to speak nicely and what they can say when they are mad. Role play how to manage when things aren’t going well with their brother or sister. Teach them how and when to ask for your help.