Bring up the patient on screen
Click Corrections -> Private Invoice -> OK
Type the amount you want to correct it. Potentially you can do either the total amount and start again or just partial - it's up to you.
Click Correction (or Discount/Write-Off/Bad-Debt, etc. as appropriate).
Type a brief reason for the correction. This will be logged along with the date & time and your username.
OK x2
You can also perform Corrections from the Invoice Copies screen however, this is a quick method that fully corrects the remaining amount for the billing (whereas the method above allows for more control).
Alternate method:
Reverse Correction (De-Correct)
In most cases you can (and should) just re-bill it.
Alternatively there is a De-Correct option in Copies. You have to enable it first in File -> General Options -> Allow Reverse Correction & Allow Correction In Copies
See also: Refund a receipt or credit