We prove a Korn-type inequality in H(Curl; Ω, ℝ ^3×3) for tensor fields P mapping Ω to ℝ ^3×3. More precisely, let Ω ⊂ ℝ ³ be a bounded domain with connected Lipschitz boundary ∂Ω. Then there exists a constant c > 0 such that, for all tensor fields P ∈ H(Curl; Ω, ℝ ^3×3), i. e., all P ∈ H(Curl; Ω, ℝ ^3×3) with vanishing tangential trace on ∂Ω. Here the rotation and tangential trace are defined row-wise. For compatible P of form P = ∇v, Curl P = 0, where v ∈ H ¹(Ω, ℝ ³) is a vector field with components v _n for which ∇v _n are normal at ∂Ω, estimates (0. 1) is reduced to a non standard variant of Korn's first inequality:, For skew-symmetric P (with sym P = 0), estimates (0. 1) generates a nonstandard version of Poincaré's inequality. Therefore, the estimate is a generalization of two classical inequalities of Poincaré and Korn. Bibliography: 24 titles.