I find the following way to remove
localhost/testmagento/index.php/parent/child.html
to
localhost/testmagento/index.php/child.html
step 1. Go to app/code/core/Mage/Catalog/Model/Url.php copy this file to app/code/local/Mage/Catalog/Model/Url.php because it is core Magento file so that we have to copy that file into the app/code/local.
Step 2: Now search for the getCategoryRequestPath($category, $parentPath) around line 698 in Magento ver. 1.9.1.0
Step 3: Search if (null === $parentPath) around line 717 and comment the line as below:
/* if (null === $parentPath) {
$parentPath = $this->getResource()->getCategoryParentPath($category);
}
elseif ($parentPath == '/'){*/
$parentPath = ''; //DO NOT Comment this line
//}
Step 4: Now Go to the Magento admin and Clear Cache System->Cache Management and Reindex System->Index Management the data.
Step 5: Refresh your browser cache and navigate again now you will see only the Sub Category in Url not the Parent Category just like as
Let me know if you have any query