Custom Exceptions!?!?

I have a class library that instantiated another class library. For sake of this conversation we will call each class library Class A and Class B

Class A instantiates Class B

Class B has a custom Exception class and will throw this exception while being constructed. The problem is, Class A never gets the exception event though the new is wrapped around a try catch block. I get a unhanded exception in the constructor of class B when I throw the exception.

For example

Class A (License Handle is Class B and has the custom exception class called LicenseNotLoaded)

try
{
     m_License = new LicenseHandle();
}
catch (LicenseNotLoaded Ex)
{
     Console.WriteLine(Ex);                           
}

Class B

public LicenseHandle()
{
     try
     {
          InitializeObjects();
     }   
     catch (LicenseNotLoaded Ex)
     {
          // Once I catch the exception, it says it's unhandled at this point when it throws.
          throw;
     }
}

What's the problem?