sitemap index points to another sitemap index

Can a sitemap index file reference another sitemap index file ?

sitemap.xml contents :

<?xml version="1.0" encoding="UTF-8"?>
<sitemapindex xmlns="http://www.google.com/schemas/sitemap/0.84">
<sitemap>
<loc>http://www.example.com/sub1/sitemap.xml</loc>
</sitemap>
<sitemap>
<loc>http://www.example.com/sub2/sitemap.xml</loc>
</sitemap>
</sitemapindex>

sub1/sitemap.xml is an index file, contents :

<?xml version="1.0" encoding="UTF-8"?>
<sitemapindex xmlns="http://www.google.com/schemas/sitemap/0.84">
<sitemap>
<loc>http://www.example.com/sub1/sub1_1/sitemap.xml</loc>
</sitemap>
</sitemapindex>