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Consider an anisotropic independent bond percolation model on the$d$-dimensional hypercubic lattice, $d\geq 2$, with parameter $p$. We show thatthe two point connectivity function $P_{p}(\{(0,\dots,0)\leftrightarrow(n,0,\dots,0)\})$ is a monotone function in $n$ when the parameter $p$ is closeenough to 0. Analogously, we show that truncated connectivity function$P_{p}(\{(0,\dots,0)\leftrightarrow (n,0,\dots,0),(0,\dots,0)\nleftrightarrow\infty\})$ is also a monotone function in $n$ when$p$ is close to 1.

A remark on monotonicity in Bernoulli bond Percolation