A Banach space X is said to have the Tsirelson property if it does not contain subspaces that are isomorphic to lp (1 ≤ p < ∞) or c 0 . The article contains a quite simple method to producing Banach spaces with the Tsirelson property.A Banach space X is said to have the Tsirelson property if it does not contain subspaces that are isomorphic to l p (1 ≤ p < ∞) or c 0 .The first example of a Banach space with such property was constructed by B.S. Tsirelson [1].The article contains a quite simple method to producing Banach spaces with the Tsirelson property. Results were communicated at the Ukrainian Mathematical Congress (August 2001, Kiev) and was announced in the Book of Abstracts of the International Conference on Functional Analysis that take place as a part of the Congress [2].