How do I disable recently closed tabs?

I do not want ANY history of where I have been to show. I cleared my history and checked that it not show anything. But I just noticed, that recently closed tabs show where I have recently been. What is the point of clearing my history or having is disabled if recently closed tabs shows where I have been. This is crucial for someone who is having their account monitored by someone else. How do I delete recently closed tabs and is there anyway to disable that?