You can install Java from http://www.java.com on your Fedora 15 desktop. Follow the steps given below:
Remove the default openjdk from your Fedora 15 installation.
Download file jdk-6u26-linux-x64-rpm.bin from http://www.java.com for Fedora 64 bit.
# chmod u+x jdk-6u26-linux-x64-rpm.bin <enter>
# ./jdk-6u26-linux-x64-rpm.bin <enter>
This will install all the rpm files.
# cd /usr/lib64/mozilla/plugins <enter>
# ln -sf /usr/java/default/jre/lib/amd64/libnpjp2.so . <enter>
Provide the link to the default java plugin from Sun.
Start firefox and in the addressbar type about:plugins
You will now see java runtime loaded in there.