Link to latest post

I would like to have a link on my static homepage that opens up my latest post. I have tried the following – which works but also displays the post at the bottom of my homepage, which I do not want. The theme is Arjuna X.

<?php query_posts('showposts=1'); ?>
<?php while (have_posts()) : the_post(); ?>
<a href="<?php the_permalink() ?>" rel="bookmark" title="Permanent Link to <?php the_title(); ?>"><?php the_title(); ?></a><br />
<?php endwhile;?>

Any ideas how to not show the post on the homepage?
Sandy