DNS dummy question

Hello everyone,

I have a some doubt about DNS. We have connected to 2 ISPs /ISP#1 and ISP#2/. Our web site's dns zone is located on ISP#1. If connection to ISP#1 is down clients won't find our website. ISP#1 connection went down few times this month.
So we are going to create our website's zone on our own DNS. Below is right way to do this?

  1. Remove zone from ISP#1
  2. Create zone on our own dns.
  3. Test

Thanks all