delete rows for tables with over one row

System ArcGIS 9.3
python 2.6

Hello

I have two kinds of point shapefiles in a folder.
Type A has only one row in the attribute table.
Type B has two rows.

Please kindly advise if there is any method using python code to delete the second row of type B shapefiles.
(P.S. The values of the second row of type B are identical to those of the row of type A)

Thank you.