So first of all Download this new Update: Android 2.3.6 Gingebread (GRK39F)
Step 1: Rename the file to update.zip.
Step 2: Connect your Nexus One to your computer and transfer update.zip to the root of your phone’s microSD card, it should not be inside any folder.
Step 3: Turn off your Nexus One.
Step 4: Keep the Volume Down button pressed and turn on the phone. Scroll down to recovery and press the power/lock button.
Step 5: You should now see a triangle with an exclamation mark. Press Power + Volume Down button.
Step 6: A menu will appear. Select sdcard:update.zip. The screen will say install from sdcard complete.
Step 7: You must now select reboot system now.
That's it after reboot your device will be updated. To check just go to go to Settings > About phone and check under Android version and Build number.
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