Sidebar still on Page, despite template

Hi everyone. I have been struggling with this problem for a few days. I want my Pages to have NO sidebar on them, and so I created this page template (named page.php). It is simply the original page.php without the line about get_sidebar() at the bottom.

Anyway, despite using this template a sidebar still appears! Can someone please help me out. I’ve included this page.php below to confirm.

Thanks.

<?php
/*
Template Name: Snarfer
*/
?>

<?php get_header(); ?>

<div id="static">

<?php if (have_posts()) : while (have_posts()) : the_post(); ?>
<div class="post">
<h3 id="post-<?php the_ID(); ?>"><?php the_title(); ?></h3>
<div class="entrytext">
<?php the_content('<p class="serif">Read the rest of this page &raquo;
'); ?>

<?php link_pages('<strong>Pages:</strong> ', '
', 'number'); ?>

</div>
</div>
<?php endwhile; endif; ?>

</div>

<?php get_footer(); ?>