  We investigate an intermittent stochastic process in which the diffusive
motion with time-dependent diffusion coefficient $D(t) \sim t^{\alpha -1}$ with
$\alpha > 0$ (scaled Brownian motion) is stochastically reset to its initial
position, and starts anew. \color{black} In the present work we discuss the
situation, in which the memory on the value of the diffusion coefficient at a
resetting time is erased, so that the whole process is a fully renewal one. The
situation when the resetting of coordinate does not affect the diffusion
coefficient's time dependence is considered in the other work of this series.
We show that the properties of the probability densities in such processes
(erazing or retaining the memory on the diffusion coefficient) are vastly
different. \color{black} In addition we discuss the first passage properties of
the scaled Brownian motion with renewal resetting and consider the dependence
of the efficiency of search on the parameters of the process.
