How do i not render a menu item on that item's page?

I have a custom menu with 9 pages in it. I have that menu displaying only on each of those 9 pages. I'd like to not render a menu item when the user is on that item's page.

So if I have a page called My Drupal in the menu along with 8 other items, I don't want My Drupal to show in the menu when on the My Drupal page. But I do want it to show on the other pages, while not showing that page's menu item.

When I say render, I mean not have it rendered in the html at all. I'm sure I can hide it with CSS but I'd prefer to simply not have it in the code to begin with.

Any suggestions?