Most traditional test generation algorithms rebuild the abstract test suite from scratch even after minimal changes to the finite state machine (FSM). New approaches have been developed to improve these methods, by identifying the effect of changes in each iteration step, and reusing as much as possible of the previous test set, and focus test generation only on modified parts of the FSM. This thesis gives an algorithm to update the Transition Tour test set after changes in a deterministic finite state machine model. This algorithm contains two main parts. The first part of the algorithm keeps an Eulerian graph up-to-date, while the second part of the algorithm maintains an Euler tour over the augmented graph. The thesis illustrates this method through examples. With a demonstration of a software design, we can see the decisions that were necessary for solving this problem. One of the expectations was platform-independent development, so the software was implemented in C++ programming language.