Intelligent Systems are served by Intelligent User Interfaces aimed to improve the efficiency, effectiveness and adaptation of the interaction between the user and the computer by representing, understanding and implementing models. The Intelligent User Interface Model (IUIM) helps to design and develop Intelligent Systems considering its architecture and its behavior. It focuses the Interaction and Dialogue between User and System at the heart of an Intelligent Interactive System. An architectural model, which defines the components of the model, and a conceptual model, which relates to its contents and behavior compose the IUIM. The conceptual model defines three elements: an Adaptive User Model (including components for building and updating the user model), a Task Model (including general and domain specific knowledge) and an Adaptive Discourse Model (to be assisted by an intelligent help and a learning module). We will show the implementation of the model by describing an application named Stigma - A STereotypical Intelligent General Matching Agent for Improving Search Results on the Internet. Finally, we compared the new model with others, stating the differences and the advantages of the proposed model.