We classify a class of 2-step nilpotent Lie algebras related to the representations of the Clifford algebras in the following way. Let $$J:{{\mathrm{\mathrm {Cl}}}}({\mathbb {R}}^{r,s})\rightarrow {{\mathrm{End}}}(U)$$ J : Cl ( R r , s ) → End ( U ) be a representation of the Clifford algebra $${{\mathrm{\mathrm {Cl}}}}({\mathbb {R}}^{r,s})$$ Cl ( R r , s ) generated by the pseudo Euclidean vector space $${\mathbb {R}}^{r,s}$$ R r , s . Assume that the Clifford module U is endowed with a bilinear symmetric non-degenerate real form $$\langle \cdot \,,\cdot \rangle _U$$ ⟨ · , · ⟩ U making the linear map $$J_z$$ J z skew symmetric for any $$z\in {\mathbb {R}}^{r,s}$$ z ∈ R r , s . The Lie algebras and the Clifford algebras are related by $$\langle J_zv,w\rangle _U=\langle z,[v,w]\rangle _{{\mathbb {R}}^{r,s}}$$ ⟨ J z v , w ⟩ U = ⟨ z , [ v , w ] ⟩ R r , s , $$z\in {\mathbb {R}}^{r,s}$$ z ∈ R r , s , $$v,w\in U$$ v , w ∈ U . We detect the isomorphic and non-isomorphic Lie algebras according to the dimension of U and the range of the non-negative integers r, s.