If you use the SQL Server 7.0 or 2000, you could read the KB, How To Move a Database Diagram .
Since the SQL Server 2005 had changed the previous setting, such as:
The diagram data is now stored in "sysdiagrams" and not "dtproperties"
"sysdiagrams" has only one row per diagram, whereas "dtproperties" has seven rows
Therefore, if you use the SQL Server 2005, I will suggest you use Mr. Ying's way to do that.