I'm using DB2 v8.1 on Linux.
I'm busy writing UDF's in Java.
Following things works fine:
I make a class-file put in the folder sqllib/function, excecute the query:
CREATE FUNCTION test(a Int) RETURNS Int EXTERNAL NAME 'udfs.multiply' LANGUAGE JAVA PARAMETER STYLE java NO SQL

When I test the function, he does what I expect it to do, so far no problem, but when I want to change the class file to update the function, just replacing te class file in the sqllib/function directory is not enough. Even when I drop the function test and create it again, he stills works with the function written in the first created class-file.
When I stop the database (db2stop) and start it again, and then create the function test again, then he takes the updated function in the new class file, but I don't like thus method.
How can I become the same result, without having to restart the database?

I suggest you read the Application Development Guide for DB2 (you can find it on the IBM web site). It explains in detail (see Chapter 21) how to build and install Java stored procedures and UDFs.

In short, to be able to dynamically replace loaded classes you should deploy them as a .jar file and use INSTALL_JAR/REPLACE_JAR functions to... well, install or replace classess.

Working with jar's instead was indeed the solution, but the REPLACE_JAR doesn't work.
The way to get it to work is as follows:

call sqlj.refresh_classes(void)
call sqlj.remove_jar('myjarke')
call sqlj.refresh_classes(void)
call sqlj.install_jar('file:/.../myudfjar.jar', 'myjarke' )
call sqlj.refresh_classes(void)

But wich ' Application Development Guide for DB2' is ment, cause none of the 3 I find on the site has 21 chapters?