Can't change title attribute in header.php

I can’t change the title of the site in the <title></title> attribute. No matter what I do, even deleting the wp_title code and changing it to <title>TEST</title>, it still posts the title as “Page title | Blog title”. It’s completely ignoring any change I make. I want it to post as “Blog title > Page title”. I tried clearing my browser cache, nothing. Anyone know why the title display won’t budge?

Thanks in advance,
Jeremy