The Unified Process (UP) is a processes framework widely known and used by the software industry and academic community. UP was developed under the conception of a universal application, but even a single process is not appropriate to address all development projects since optimal process depends on the particularities of each project or organization. Frequently, many process components need to be adapted to the organization or project needs, a complex task because the experience and knowledge required. Perform adaptation in an inappropriate way is prone to error due to the difficulties for taking tailoring decisions. The paper goal is proposing a canonical software processes family based on the Unified Process to support software process tailoring. Our methodology was based on the meta-process CASPER to build a software process family and we use the Case Study method as a strategy for validating the canonical process family empirically. As a result, we show a canonical software processes family, which will serve as a platform for determining a process family based on Unified process in a small software organization. This canonical family has the advantage that uses a tailoring mechanism following a transformation strategy that encapsulates tailoring decisions in order to systematize this activity. In this work, we show the initial results in the applicability of a canonical software process family as base in the building the software process families based on UP in the small companies context, and also we conclude that the UP is a process framework with spread spectrum, which limited its formulation like a general software process family, due to that a process family requires determining carefully the application domain known as software process family scope