The muqarnas is an architectural form developed and used in Islamic architecture over the last millennium. In short it can be defined as: a three-dimensional form, whose visual function is the gradual transition between two levels, two sizes, and or two shapes. One of the methods of its production, which prevailed in the Islamic western lands, involved the use of certain sets of pre-designed units, that when combined in different ways generate a very wide range of alternatives. The plans of these units are based on shapes of 45-, 90-, 135- degrees. Thus, they are limited in their final output; and their innovativeness was long lost accordingly. The main objective of this paper is to create a new set (or sets) of units that belong to the same logic of these described but overcome their limitations. The method is first to analyze the available units, second to reach the minimum number of units that can be considered as the generic units, third to synthesize their origin of creation (as it is not found in any literature) and thus creating a system of unit-generation, and finally to create the new sets of units. These sets can be considered as a new evolutionary step of the muqarnas of this type. Accordingly, a computer program for the unit creation was created to test and evaluate the concepts presented in the paper.