Given that you are in a position where anything filed outside your personal control might be destroyed by someone else, and given that you are probably still expected to have access to this information whether destroyed or not, I suggest you keep your own notebook.
A couple of further suggestions:
When you buy your notebook, buy a good-quality one. Think Moleskine. A little expensive, yes; but others will be less likely to rip pages out of it, or "borrow" it, or set their nasty, dripping coffee mug on top of it.
Immediately after purchase, put page numbers on the top of every page (or at a minimum, every other page).
Take notes chronologically. Do not skip pages. Write the date at the top of each page. Start a new page each day if you like, but I usually just skip a few lines and write the date to indicate a new day. If you absolutely must have a blank page somewhere, draw a giant X through the page so you know you did it on purpose.
After a day or two of note-taking, go to the very last page of the notebook, and start an index. Each entry should contain the page number, and enough information for you to find what you need later. For example:
1. Watson Project - Request for new assistant
2 - 5. Watson Project - Notes from zoning meeting
6. (Blank Page)
7. Microsoft Word - Locations of form templates and passwords
8. Watson Project - boss commits to giving me a promotion when done
When you get to the bottom of the last page, continue the index on the second-to-last page.
Do not keep personal notes in here. If you need to, keep a separate personal notebook and reference items between the notes. For example, you might write a note like this:
Today, Mr. Boss promised me a raise at the conclusion of this project [specifics of raise in personal notebook, page 72].
This will give you the flexibility to leave the notebook to your successor when you leave.
I started doing this a year ago, and it has made a world of difference.