[xsl] xsl:processing-instruction not processed

[Jan <janusius@xxxxxxx>]

Dear list,

I would like to achieve the following with xslt:

I have one xsd and two stylesheets. I'd like to transform the xsd in two 
steps.
I am processing the xsd file to generate xml with the first xsl and I am 
adding a xsl:processing-instruction like this:

  <xsl:processing-instruction name="xml-stylesheet">
    <xsl:text>type="text/xml" href="second.xsl"</xsl:text>
  </xsl:processing-instruction>

My idea was that the result of the first transformation would than 
transformed again by applying the second xsl added as 
xsl:processing-instruction. But only the first transformation is applied.
I have tried it with Chrome (simply by opening the local xsd file).

Is it Chrome's processor or is my idea simply wrong?

Thank you
Jan