Let X$_1$, X$_2$,... be a sequence of independent and identically distributed random variables with continuous cumulative distribution function F(x). X$_j$ is an upper record value of this sequence if X$_j$ > max {X$_1$,X$_2$,...,X$_{j-1}$}. We define u(n)=min{j$mid$j> u(n-1), X$_j$ > X$_{u(n-1)}$, n $geq$ 2} with u(1)=1. Then F(x) = 1-x$^{ heta}$, x > 1, ${ heta}$ < -1 if and only if (${ heta}$+1)E[X$_{u(n+1)}$$mid$X$_{u(m)}$=y] = ${ heta}E[X_{u(n)}$mid$X_{u(m)}=y], ( heta+1)^2E[X_{u(n+2)}$mid$X_{u(m)}=y] = heta^2E[X_{u(n)}$mid$X_{u(m)}=y], or ( heta+1)^3E[X_{u(n+3)}$mid$X_{u(m)}=y] = heta^3E[X_{u(n)}$mid$X_{u(m)}=y], n $geq$ M+1$</TEX>.