Dear Rolland,
You should go to that blog dashboard, then click on:
1) Design;
2) Templates;
3) Under 'Quickfilters': Template Modules
4) Header;
5) Remove from that 'Header' template module:
CODE
<$mt:Include widget="Search" $>
Then save and click on the two rounded arrows from the movable type admin top menu (Publish Site).
Enjoy the trick

Kind Regards,
Mihai Bocsaru