We present a new variant of the secretary problem. Let $A$ be a totally ordered set of $n$ \emph{applicants}. Given $P\subseteq A$ and $x\in A$, let $rr(P,x)=\vert\{z\in P \mid z\leq x\}\vert\mbox{ }$ be the \emph{relative rank of} $x$ \emph{with regard to} $P$, and let $rr_n(x)=rr(A,x)$. Let $x_1,x_2,\dots,x_n\in A$ be a random sequence of distinct applicants. The aim is to select $1<j\leq n$ such that $rr_n(x_{j-1})-rr_n(x_j)\in\{-1,1\}$. Let $α$ be a real constant with $0<α<1$. Suppose the following stopping rule $τ_n(α)$: reject first $αn$ applicants and then select the first $x_j$ such that $rr(P_j,x_{j-1})-rr(P_j,x_j)\in\{-1,1\}$, where $P_j=\{x_i\mid 1\leq i\leq j\}$. Let $p_{n,τ}(α)$ be the probability that $τ_n(α)$ selects $x_j$ such that $rr_n(x_{j-1})-rr_n(x_j)\in\{-1,1\}$. We show that \[\lim_{n\rightarrow\infty}p_{n,τ}(α)\leq \lim_{n\rightarrow\infty}p_{n,τ}\left(\frac{1}{2}\right)=\frac{1}{2}\mbox{.}\]