Transactional memory (TM) systems implement the concept of an atomic execution unit called a transaction in order to discharge programmers from explicit synchronization management. But when shared data is atomically accessed by both transaction and non-transactional code, a TM system must provide strong isolation in order to overcome consistency problems. Strong isolation enforces ordering between non-transactional operations and transactions and preserves the atomicity of a transaction even with respect to non-transactional code. This paper presents a TM algorithm that implements strong isolation with the following features: (a) concurrency control of non-transactional operations is not based on locks and is particularly efficient, and (b) any non-transactional read or write operation always terminates (there is no notion of commit\abort associated with them).