Prova cosi

codice:
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">

<html>
<head>
<title>Untitled</title>
<script language="JavaScript" type="text/javascript">
<!--
function antitag(){
    temp=document.getElementById('mioTesto').value;
    if (temp.indexOf('>')>-1 || temp.indexOf('<')>-1){
      alert('< o > sono male');
      return false;
    }
  return true;
}
//-->
</script>

</head>
<body>
<form name="mioForm" action="pagina_di_invio.php" method="post" onsubmit="return antitag()">
 <textarea id="mioTesto"></textarea>
 

 <input type="submit" value="Invia">
</form>
</body>
</html>