  Let $X_1,~X_2,\cdots$ be a sequence of i.i.d random variables which are
supposed to be observed in sequence. The $n$th value in the sequence is a
$k-record~value$ if exactly $k$ of the first $n$ values (including $X_n$) are
at least as large as it. Let ${\bf R}_k$ denote the ordered set of $k$-record
values. The famous Ignatov's Theorem states that the random sets ${\bf
R}_k(k=1,2,\cdots)$ are independent with common distribution. We introduce one
new record named $recent-k-record$ (RkR in short) in this paper: $X_n$ is a
$j$-RkR if there are exactly $j$ values at least as large as $X_n$ in
$X_{n-k},~X_{n-k+1},\cdots,~X_{n-1}$. It turns out that RkR brings many
interesting problems and some novel properties such as prediction rule and
Poisson approximation which are proved in this paper. One application named "No
Good Record" via the Lov{\'a}sz Local Lemma is also provided. We conclude this
paper with some possible connection with scan statistics.
