need little help of bug fixers.

[GCDEF]

I don't understand what you say in first paragraph.
but if you want that catch should do nothing just keep it's original value then it is more simpler see it

 // Overloaded assignment operator for CMessage objects
    CMessage& operator=(const CMessage& aMess)
    {
char arr[](pmessage);  //will it work error may pointer to char conversion invalid
      try
{
      if(this == &aMess)               // Check addresses, if equal
        return *this;                  // return the 1st operand

      // Release memory for 1st operand
      delete[] pmessage;
      pmessage = new char[strlen(aMess.pmessage) + 1];
     
      // Copy 2nd operand string to 1st
      strcpy_s(this->pmessage, strlen(aMess.pmessage) + 1, aMess.pmessage);

      // Return a reference to 1st operand
      return *this;
}
catch(bad_alloc &ex)
  {
    cout << "Memory allocation failed." << endl
         << "The information from the exception object is: "
         << ex.what() << endl;
cout<<"making no change\n";
pmessage=new char[strlen(arr)+1];
strcpy_s(pmessage,strlen(arr)+1),arr);
  }
}

what about this.

One more time, in addition to Paul's comments, an = operator shouldn't contain any cout statements. Typically the user wouldn't want to see them or have any idea what to do about it. When something goes wrong, it should be up to the caller of that function to determine how to handle the error. All your function should do is indicate somehow to its caller that something has gone wrong, and provide a way for the caller to determine what. Exceptions are designed to provide just such a mechanism.