In this paper we show how to study under the self-similarity hypothesis a perfect fluid Bianchi I model with variables G and Λ, but under the condition div T≠0. We arrive to the conclusion that: G and Λ are decreasing time functions (the sign of Λ depends on the equation of state), while the exponents of the scale factor must satisfy the conditions [Formula: see text] and [Formula: see text], ∀ω ∈ (-1, 1), relaxing in this way the Kasner conditions. We also show the connection between the behavior of G and the Weyl tensor.