Adobe Flash Player download

Have two machines - Toshiba Sat L550 laptop running 7 Pro and have the Flash Player (10) on it. Now have a new desky running Home Premium (both 64bit OS's) while the laptop had the Flash P on it I cannot for the life of me download Flash onto the desktop from the net.
I have tried copying the Flash to a usb stick and pasting / transferring the app to the desktop - as I did the Reader (it wouldn't download either) but it just sits there doing nothing.
Download is telling me that Flash in 64bit is not available (Australia) so am left with no Youtube or anything that requires Flash for video / graphics.
So any advice would be more than appreciated with the proviso that I don't like third party downloads - too many problems experienced already.

Ok I'll try that but going on previous attempts I'm not going to hold my breath - well not for too long lol!!

Hey Hopalong have downloaded the 64bit version from
Adobe Labs - Downloads: Flash Player "Square" Preview Release
and mate it works am now listening to some really nice finger picking guitar on YT (young bloke - Delgift if you like that sort of stuff - deos other and is really talented) but I digress (bad habit but at least I won't go blind eh lol!!).

Thanks so much again!!

Joh

Didn't know it was here and so glad I found it! - great fins.

IC aka Joh

Thanks Mike I haven't tried Chrome yet but might as long as it isn't crammed with all those fancy doo dads - hate clutter.

I might also just have a look at the Shockwave feature too - as I am not aware of what it actually does but a Google will take of that eh?

Cheers!
John