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First, right-click on the up arrow as demonstrated in the snapshot below. Next, hover your mouse pointer over the "Search" (or "Cortana") option, then a submenu will appear.
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Choose "Hidden" here to disable the taskbar search altogether, or select "Show icon" to reduce the search bar down to a small icon.Choose "Hidden" here to disable the taskbar search altogether, or select "Show icon" to reduce the search bar down to a small icon.
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Congrats!! You've removed the search bar.