AFAIK, Apple doesn't provide a mechanism to do that; to entirely remove Java. (Java was an integrated component of OS X in most releases prior to 10.7, and didn't become an optional component until 10.7.)
The usual advice is to disable or delete the JVM web start plug-ins in all web browsers. Here is the Apple Safari sequence.
In recent OS X versions, the plug-in is usually here /Library/Internet\ Plug-Ins/JavaAppletPlugin.plugin though I don't have a 10.4 box to check that.
I'd also tend to doubt a typical JVM attack would work all that well on a PPC-class 10.4 box, for that matter.
Renaming the directory containing the Java frameworks would likely work, though what that brute-force might do for something around that does need Java or that does try to upgrade Java... who knows? Here's a few details on the old setup, but it doesn't list 10.4.
Douglas McNeill wrote:
I'm trying to remove the Java install for security reasons. Can't figure out how to do it.
I don't recommend you do that for a variety of reasons.
It's time consuming and difficult and could cripple your OS as it's integrated into the System.
Other than Java browser use, basic Java for desktop use has few vulnerabilities and none has ever been exploited on a Mac. Disabling it in all your browsers will provide sufficient protection and removing the plugin is the most I would ever recommend.