Domain mapping to sub-folders

I have a website and it’s domain lets say is http://www.mydomain.com, it is not a wordpress website.
I’ve also created a website for a client which is located in http://www.mydomain.com/client1,
this is a wordpress based website and that is the root directory for it.
Now when I map http://www.client1.com to http://www.mydomain.com/client1 and type http://www.client1.com in the address bar everything is ok, homepage for my clients website is displayed fine and the url is correct i.e. http://www.client1.com. However when I click on the contact us page (or any other page or post) it goes to http://www.mydomain.com/client1/contact, but I want it to goto http://www.client1.com/contact. I’ve tried changing the website URL settings under General on the WP dashboard but no luck. If I change the site address to http://www.client1.com it displays the homepage ok but when I click on any links it says the server is not configured correctly. Please help .