There is the only better way is AJAX as everyone is suggest in their posts. The alternative is using IFrames like below:
<iframe name="f1" id="f1"> </iframe>
<a href='yourpage.php' target='f1'>Click </a>
Now you will get the output in IFrame (you can place IFrame wherever you need in the page or event hide it and the result from the script).
Hope for non Ajax solution this is better.