CDATA help

Friends,
  I am trying to *generate a XSLT stylesheet* with XSLT. Below is my attempt.

<?xml version="1.0" encoding="UTF-8"?>
<xsl:stylesheet version="1.0" xmlns:xsl="http://www.w3.org/1999/XSL/Transform">
  
  <xsl:output method="xml" indent="yes" omit-xml-declaration="yes" />    
  
  <xsl:template match="/">
     <![CDATA[
       <?xml version="1.0" encoding="UTF-8"?>
       <xsl:stylesheet version="1.0"
xmlns:xsl="http://www.w3.org/1999/XSL/Transform">
     ]]>
     
     <![CDATA[
       </xsl:stylesheet>
     ]]>
  </xsl:template>  
  
</xsl:stylesheet>

I thought CDATA section was neccessary to output these instructions ..
<?xml version="1.0" encoding="UTF-8"?>
<xsl:stylesheet version="1.0" xmlns:xsl="http://www.w3.org/1999/XSL/Transform">
etc..

But this is giving me output -

&lt;?xml version="1.0" encoding="UTF-8"?&gt;
&lt;xsl:stylesheet version="1.0" xmlns:xsl="http://www.w3.org/1999/XSL/Tr
ansform"&gt;

&lt;/xsl:stylesheet&gt;

The output is having characters &lt; &gt; etc. But I want the output as
<?xml version="1.0" encoding="UTF-8"?>
<xsl:stylesheet version="1.0" xmlns:xsl="http://www.w3.org/1999/XSL/Transform">

</xsl:stylesheet>

How I can do this?

I am also curious why with my above stylesheet the output is showing
&lt; &gt; and not < > ?

Also is there any better approach?

Thanks for your help.