Magento redirecting to old URL after duplicating site

On sitea.com, you might want to take a look at its database and the core_config_data table for the base URL. OR, you could try and execute the following query:

UPDATE `core_config_data` SET `value`='http://sitea.com/' WHERE `value` LIKE 'http://%' LIMIT 2;

do the same on siteb.com’s database for good measure

UPDATE `core_config_data` SET `value`='http://siteb.com/' WHERE `value` LIKE 'http://%' LIMIT 2;