  Recently, in ["The coin-turning walk and its scaling limit", Electronic
Journal of Probability, 25 (2020)], the ``coin-turning walk'' was introduced on
${\mathbb Z}$. It is a non-Markovian process where the steps form a (possibly)
time-inhomogeneous Markov chain. In this article, we follow up the
investigation by introducing analogous processes in ${\mathbb Z}^d$, $d\ge 2$:
at time $n$ the direction of the process is ``updated'' with probability $p_n$;
otherwise the next step repeats the previous one. We study some of the
fundamental properties of these walks, such as transience/recurrence and
scaling limits.
  Our results complement previous ones in the literature about ``correlated''
(or ``Newtonian'') and ``persistent'' random walks.
