  We classify multidimensionally consistent maps given by (formal or
convergent) series of the following kind: $$ T_k x_{ij}=x_{ij} +
\sum_{m=2}^\infty A_{ij ; \, k}^{(m)}(x_{ij},x_{ik},x_{jk}), $$ where $A_{ij;\,
k}^{(m)}$ are homogeneous polynomials of degree $m$ of their respective
arguments. The result of our classification is that the only non-trivial
multidimensionally consistent map in this class is given by the well known
symmetric discrete Darboux system $$ T_k
x_{ij}=\frac{x_{ij}+x_{ik}x_{jk}}{\sqrt{1-x_{ik}^2}\sqrt{1-x_{jk}^2}}. $$
