On your Dashboard, select Layout. This will take you to the Template tab. Click Edit HTML. Under the Edit Template section you will see you blog's HTML.

[blogspot border]

Step 2:
Look for tags #header-wrapper and #header as below and change border to 0 then SAVE Template

#header-wrapper {
width:660px;
margin:0 auto 10px;
border:0px solid $bordercolor;
}

#header {
margin: 5px;
border: 0px solid $bordercolor;
text-align: center;
color:$pagetitlecolor;
}

Step 3: Add this code anywhere...

#navbar-iframe {
height:0px;
visibility:hidden;
display:none
}

done!