Does child support order change when a second child is born?

If a person who pays child support has a baby with a new partner does the CS for the older child get reduced because the payer has to also support the new child even though new child lives in household with payer?
Unfortunately no, the child that is the last to be born is the one that really has the least of rights. It may not be fair but the Court always has the interest of the child who is getting the child support. There are many of children who currently suffer because a percentage of money is sent to another house hold. So the best interest of the child is bias.