The dedicated machine constraint for the photolithography process in semiconductor manufacturing is one of the new challenges introduced in photolithography machinery due to natural bias. With this constraint, the wafers passing through each photolithography process have to be processed on the same machine. The purpose of the limitation is to prevent the impact of natural bias. However, many scheduling policies or modeling methods proposed by previous research for the semiconductor manufacturing system have not discussed the dedicated machine constraint. We propose the Load Balancing (LB) scheduling method based on a Resource Schedule and Execution Matrix (RSEM) to tackle this constraint. The LB method uses the RSEM as a tool to represent the temporal relationship between the wafer lots and machines. The LB method is to schedule each wafer lot at the first photolithography stage to a suitable machine according to the load balancing factors among photolithography machines. In the paper, we present an example to demonstrate the LB method and the result of the simulations to validate our method.