OK - now I forgot to also post the derivative file of the pyuic4. After I had designed the layout with QT Designer, I created the following tstMain.py file via pyuic4:

Qt Code: 
  1. # -*- coding: utf-8 -*-
  2.  
  3. # Form implementation generated from reading ui file 'tstMain.ui'
  4. #
  5. # Created: Sun Sep 30 21:39:12 2007
  6. #      by: PyQt4 UI code generator 4.3
  7. #
  8. # WARNING! All changes made in this file will be lost!
  9.  
  10. from PyQt4 import QtCore, QtGui
  11.  
  12. class Ui_tstMain(object):
  13.     def setupUi(self, tstMain):
  14.         tstMain.setObjectName("tstMain")
  15.         tstMain.setEnabled(True)
  16.         tstMain.resize(QtCore.QSize(QtCore.QRect(0,0,951,394).size()).expandedTo(tstMain.minimumSizeHint()))
  17.  
  18.         sizePolicy = QtGui.QSizePolicy(QtGui.QSizePolicy.Preferred,QtGui.QSizePolicy.Preferred)
  19.         sizePolicy.setHorizontalStretch(0)
  20.         sizePolicy.setVerticalStretch(0)
  21.         sizePolicy.setHeightForWidth(tstMain.sizePolicy().hasHeightForWidth())
  22.         tstMain.setSizePolicy(sizePolicy)
  23.         tstMain.setLayoutDirection(QtCore.Qt.LeftToRight)
  24.  
  25.         self.centralwidget = QtGui.QWidget(tstMain)
  26.         self.centralwidget.setObjectName("centralwidget")
  27.  
  28.         self.tbl_OpenFile = QtGui.QTableWidget(self.centralwidget)
  29.         self.tbl_OpenFile.setGeometry(QtCore.QRect(110,80,811,121))
  30.  
  31.         sizePolicy = QtGui.QSizePolicy(QtGui.QSizePolicy.Expanding,QtGui.QSizePolicy.Expanding)
  32.         sizePolicy.setHorizontalStretch(0)
  33.         sizePolicy.setVerticalStretch(0)
  34.         sizePolicy.setHeightForWidth(self.tbl_OpenFile.sizePolicy().hasHeightForWidth())
  35.         self.tbl_OpenFile.setSizePolicy(sizePolicy)
  36.         self.tbl_OpenFile.setMaximumSize(QtCore.QSize(16777215,16777215))
  37.         self.tbl_OpenFile.setLineWidth(1)
  38.         self.tbl_OpenFile.setObjectName("tbl_OpenFile")
  39.  
  40.         self.btn_OpenFile = QtGui.QPushButton(self.centralwidget)
  41.         self.btn_OpenFile.setGeometry(QtCore.QRect(20,80,81,23))
  42.         self.btn_OpenFile.setObjectName("btn_OpenFile")
  43.  
  44.         self.tbl_ListShow = QtGui.QTableWidget(self.centralwidget)
  45.         self.tbl_ListShow.setGeometry(QtCore.QRect(20,260,901,81))
  46.         self.tbl_ListShow.setObjectName("tbl_ListShow")
  47.  
  48.         self.btn_SetWorkingDir = QtGui.QPushButton(self.centralwidget)
  49.         self.btn_SetWorkingDir.setGeometry(QtCore.QRect(20,50,82,23))
  50.         self.btn_SetWorkingDir.setObjectName("btn_SetWorkingDir")
  51.  
  52.         self.lnEdt_WorkingDir = QtGui.QLineEdit(self.centralwidget)
  53.         self.lnEdt_WorkingDir.setEnabled(True)
  54.         self.lnEdt_WorkingDir.setGeometry(QtCore.QRect(110,50,811,20))
  55.         self.lnEdt_WorkingDir.setAutoFillBackground(False)
  56.         self.lnEdt_WorkingDir.setReadOnly(True)
  57.         self.lnEdt_WorkingDir.setObjectName("lnEdt_WorkingDir")
  58.  
  59.         self.btn_ListShow = QtGui.QPushButton(self.centralwidget)
  60.         self.btn_ListShow.setGeometry(QtCore.QRect(730,230,191,23))
  61.         self.btn_ListShow.setObjectName("btn_ListShow")
  62.         tstMain.setCentralWidget(self.centralwidget)
  63.  
  64.         self.menubar = QtGui.QMenuBar(tstMain)
  65.         self.menubar.setGeometry(QtCore.QRect(0,0,951,21))
  66.         self.menubar.setObjectName("menubar")
  67.         tstMain.setMenuBar(self.menubar)
  68.  
  69.         self.statusbar = QtGui.QStatusBar(tstMain)
  70.         self.statusbar.setObjectName("statusbar")
  71.         tstMain.setStatusBar(self.statusbar)
  72.  
  73.         self.retranslateUi(tstMain)
  74.         QtCore.QMetaObject.connectSlotsByName(tstMain)
  75.  
  76.     def retranslateUi(self, tstMain):
  77.         tstMain.setWindowTitle(QtGui.QApplication.translate("tstMain", "My Test Application", None, QtGui.QApplication.UnicodeUTF8))
  78.         self.tbl_OpenFile.setRowCount(0)
  79.         self.tbl_OpenFile.clear()
  80.         self.tbl_OpenFile.setColumnCount(0)
  81.         self.tbl_OpenFile.setRowCount(0)
  82.         self.btn_OpenFile.setText(QtGui.QApplication.translate("tstMain", "Open File", None, QtGui.QApplication.UnicodeUTF8))
  83.         self.tbl_ListShow.clear()
  84.         self.tbl_ListShow.setColumnCount(0)
  85.         self.tbl_ListShow.setRowCount(0)
  86.         self.btn_SetWorkingDir.setText(QtGui.QApplication.translate("tstMain", "Set Working Dir", None, QtGui.QApplication.UnicodeUTF8))
  87.         self.lnEdt_WorkingDir.setText(QtGui.QApplication.translate("tstMain", "Working Directory NOT yet set !", None, QtGui.QApplication.UnicodeUTF8))
  88.         self.btn_ListShow.setText(QtGui.QApplication.translate("tstMain", "Show List", None, QtGui.QApplication.UnicodeUTF8))
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OK - Once I run the main.py file I am presented with the option to load a file in the first QTableWidget and I do so. In this way, the first QTableWidget named tbl_OpenFile is full of numbers imported from the opened file.
I then try to select whole columns here and there clicking with the mouse on the headers of the table. And so it does - the columns are selected...

...but when I click on the button btn_ListShow responsible to transfer my selection to the last QTable Widget named tbl_ListShow, I get the aforementioned error.

Thanx again,
Thomas