Let (X, +) denote (R, +) or (2 ω , + 2 ). We prove that for any meagre set F ⊆ X there exists a subgroup G ≤ X without the Baire property, disjoint with some translation of F . We point out several consequences of this fact and indicate why analogous result for the measure cannot be established in ZFC. We extend proof techniques from [1].2010 Mathematics Subject Classification: Primary 28A05, 54E52. Key words and phrases: non-measurable subgroup, Baire property, algebraic sum.Proof. The first part easily follows from the definitions. For the proof of the second part, assume we have a z ∈ D ∞ with the property that φ(z)+ρ = φ(g 1 ) + φ(g 2 + 2 v), for some g 1 , g 2 ∈ G and ρ ∈ {0, 1}. We'll show that z ∈ G + 2 v.Let m 1 , m 2 < ω satisfy U n<ω g i ↾ [a n , b n − m i ] ≡ 0, for i = 0, 1, and m = max{m 1 , m 2 }. Then