  State of a $d$-dimensional quantum system can only be inferred by performing
an informationally complete measurement with $m\geqslant d^2$ outcomes.
However, an experimentally accessible measurement can be informationally
incomplete. Here we show that a single informationally incomplete measuring
apparatus is still able to provide all the information about the quantum system
if applied several times in a row. We derive a necessary and sufficient
condition for such a measuring apparatus and give illustrative examples for
qubits, qutrits, general $d$-level systems, and composite systems of $n$
qubits, where such a measuring apparatus exists. We show that projective
measurements and L\"{u}ders measurements with 2 outcomes are useless in the
considered scenario.
