In Windows XP you must enable East Asian languages. In Windows 7 and Vista, East Asian languages are enabled by default.
Install this update after Language Packs / MUI Packs for Windows or Office to avoid replacing this update with older IME files.
Go to this Microsoft download page:
Although that page is titled "Microsoft Office 輸入法 2010", don't worry if you have a different version of Office or don't have Office at all. You'll still be able to install this. You can also ignore the omission of Vista and XP sp3: it works on those as well as Windows 7. (It does not work in Windows 8 or later.)
Click the "下載" ("Download") button:
On the next page, select the appropriate version for your system: x64 for 64-bit systems, or x86 for 32-bit systems.
After you download the file, double-click, install and you're done...unless you get an error message.
If your installation isn't stopped by an error message, you can skip this section and scroll on down. For a while this was fixed, but it may have returned. If you do see this error message, read on...
The first time I clicked the installer, I got the very cryptic "You don't need this" message shown here. ---->
Someone at Microsoft keeps releasing IME update installers that look for Office on your system.
I think Office is distributed in Chinese markets with Chinese language packs containing the latest IME updates, and so if it sees Office the installer assumes you already have the update. I got them to fix this once in the Taiwan/HK IME updater, but now it's back - in both the Taiwan/HK and mainland/Singapore versions!
If you have Office 2013, you may see a different error about missing IME64.cab or IME32.cab files.
Solution: I've extracted the main .MSI installer files for all of you, kept the old .cab files in the folder for anyone with a newer version of Office,
and deleted the rest. So, if you don't mind downloading installation files from my site, here are the 32-bit and 64-bit versions with that problem removed:
Download IME2010_zh-tw_MSI-and-cabs-only.zip (136 MB)