Not refreshing dependent drop down (AJAX)

I have a listing webiste and when submitting a listing you need to choose the category/subcategory which causes an anoying page refress. I need a fix to avoid this page refresh hopefully using AJAX. The site where you can check this: [login to view URL] you can login with: user: test pw:1234567 After login click: "Regisztráció" then "Ingyenes" then in the first drop down you can select the category which refresshes to give subcategories.