its because you have an if statement that displays the arrow and a link to the second page...if you are on page[0]...
you should make it like
$sql = query to make list
$results = mysql_num_rows($sql);
//To display link to Next page : current page is 1 for first, 2 for second, etc, not 0 for the first page
if(($results/$current_page) > $results_per_page)
{show link to next page}
//To display link to previous page
if($current_page > 1)
{go to previous page, only shows up if you arent on the first page}
This way, if the result is 49 and you want to show 25 results per page, if you are on page one, the if is true, if you are currently on page 2, its not, and thus, the link wont be displayed...