Found the solution at here : http://forums.fedoraforum.org/showthread.php?p=1185767
Howto: Install Skype (dynamic) on Fedora 10 64-bit
I downloaded and installed Skype on Fedora 10, 64-bit, and it came up just fine.
I recommend the dynamic version, since it makes use of the existing system libraries that are managed by Fedora. This will minimize any potential library conflicts.
All that is needed is to make sure you have all the 32-bit versions of the libraries Skype requires.
Using the "ldd" command, I analyzed the library requirements of the "skype" program. So that you don't also have to do this, I crunched the results into a giant yum command.
Become root (enter root's password when prompted):
Now that you are root, cut and paste this, all on one line:
yum install alsa-lib.i386 dbus-libs.i386 e2fsprogs-libs.i386 expat.i386 fontconfig.i386 freetype.i386 glib2.i386 glibc.i686 keyutils-libs.i386 krb5-libs.i386 libcap.i386 libgcc.i386 libICE.i386 libpng.i386 libselinux.i386 libSM.i386 libstdc++.i386 libX11.i386 libXau.i386 libxcb.i386 libXcursor.i386 libXdmcp.i386 libXext.i386 libXfixes.i386 libXi.i386 libXinerama.i386 libXrandr.i386 libXrender.i386 libXScrnSaver.i386 libXv.i386 openssl.i386 qt.i386 qt-x11.i386 zlib.i386
The yum command should be all on a single line!
Scroll all the way to the right, if you have to, in order to cut and paste the entire line all at once.
Please ignore the little ":" mark I put at the bottom. I had to do that, in order to work around a forum bug that was making it difficult to cut and paste a very long single line.
Every library is "i386" version, except for glibc, which strangely is "i686".
Answer "yes" to any questions the yum command asks you for, if prompted.
Assuming it works, close that terminal window. You don't need to be root anymore:
Now, you can install the dynamic version of Skype, and it should work. Go here:
Choose "Dynamic", near the lower left of the box in the middle of the page.
You will download this file:
Now, open up a new terminal window, and "cd" into the directory that you downloaded Skype into, and extract and run Skype.
I'm assuming it's your Desktop. If you downloaded the file somewhere else, change these instructions accordingly.
Here's commands to run, as a normal user (be sure you have closed your old root window first, you don't need to be root anymore, and in fact it will cause problems if you try to run Skype as root):
tar -jxvf skype-220.127.116.11.tar.bz2
The Skype program should come right up, since you now have all the libraries.
Log in. Skype should now be up and running.
In the main Skype window, hit the "S" in the lower left corner to bring up the menu, then choose Options.
Skype sound device setting:
In Skype, go to Sound Devices. I recommend setting your sound devices to something that contains "plughw:default,0" in its name. Do this for all 3 choices: sound in, sound out, and ringing. Choose the name of your device that best matches the hardware you want to use. Definitely avoid generic single-word names like "default", "hdmi", "pulse", and so on.
Make sure the "Make a test sound" button works. If you can't hear anything, your sound device might have began muted, we fix that next.
Fedora volume control setting:
In the main GNOME desktop menu (upper left area of your screen), open System/Preferences/Hardware/Volume Control. Choose the name of your hardware that matches what you chose in Skype, with "(Alsa mixer)" at the end of it. Avoid choosing anything that has the name "(OSS mixer)" or "(PulseAudio mixer)" in it!
The volume control window appears. Click on Playback. Crank volume to 100%. If there's an "X" in the speaker icon just below the volume control, click on it, to unmute the sound. Now click on Recording. Crank volume to 100%. If there's an "X" in the speaker icon or the microphone icon just below the volume control, again, click on them to unmute the sound. There should be no "X" anywhere, in either playback or recording.
Now, Skype "Test Sound" should work. If it's too loud, adjust volume to your preferences.
Skype video settings:
In Skype, go to Video Devices. Try selecting your webcam from the list, and hit Test. It worked for me the first time! Fedora has really improved their webcam support in this latest release. Almost every known webcam should work now.
Now, you're ready to make a call. Call "echo123" first, to make sure your sound works. Call your friends, to make sure your video works
Running Skype easier, as a clickable desktop icon:
I'll leave this for somebody else to fill in. One thing that's important, you must "cd" to the directory where Skype was installed to! If you aren't in that directory when you run Skype, then Skype won't be able to access any of its built-in resources, so things like ringtones and other sound effects won't work.
Running Skype at startup, automatically:
Again, I'll leave this for somebody else to fill in. I never did get the hang of running things at startup under GNOME....