Nowadays, many signal processing activities are related to the orthogonal properties of specific signals. However, only a few methods offer an analytical solution for generating orthogonal signals, especially when only one input to the generating system is available. These methods are often related to very specific applications and lack generalization. In this paper, the use of the Gram-Schmidt orthogonalization process combined with simple transformation operators is proposed as a new framework for generating orthogonal signals. The objective is to provide a rigorous, clear and simple procedure capable of deriving multiple orthogonal signals from a single input. Many examples are discussed to better illustrate the novelty of the method and the main results.