After the construction of the Schlachschiff H was stopped in 1939, the Kriegsmarine continued to develop plans for new battleships. Although most of those plans were only desgin studies and never intented to be build, some of those plans reached a level that could be used for the construction of those ships.
One of the design studies was the Schlachschiff Design 40A made in 1940. Based on the H39 design, this ship was slightly bigger in size, but should have carried only 6 guns in its main artillery. It is not known for sure, which gun size was planned for this design, but the idea was to use bigger guns than the 40,6 cm ones of the H39. Besides the main artillery, the armament of the H40A was similar to the one of the H39.
Another difference was the used of a mixed propulsion system, two fo the four shafts should be driven by diesel engines, the other two by steam turbines, this resulted in a much higher engine performance and to speed for the ship.