Add a Gadget and look for Search Box. Edit the ¨Navbar¨ gadget, and select ¨Off.¨ When you do this you will also loose the Blog Search window. If you want a Search window go to Layout and add it as a Gadget in the Sidebar. Click on
Select your preferences as to what you want your Search box to search.
Once you have done this you will not have the Next Blog on top of your header and people will not run into your blog by accident, unless you want people to find you then you can leave it there.