Creating an Instance with Wordpress from AMI Issue

I created an EC2 instance which I associated with an Elastic IP#1 address and on which I installed a LAMP stack and a Wordpress (precisely in that order). It is working well. What I would like to have is a precise copy of this site (for development purposes) that points to a different Elastic IP#2 address.

When I create an AMI of the original site, launch an Instance from it and associate it with a new Elastic IP#2, it seems to be working fine when I type that IP in the browser. However, if I click on any of the links, it opens the page on the site under Elastic IP#1. Does this mean Wordpress saved the host address somewhere in the database? How can I resolve this?