  Harrow-Hassidim-Lloyd algorithm (HHL) allows for the exponentially faster
solution of a system of linear equations. However, this algorithm requires the
postselection of an ancilla qubit to obtain the solution. This postselection
makes the algorithm result probabilistic. Here we show conditions when the HHL
algorithm can work without postselection of ancilla qubit. We derive
expectation values for an observable $M$ on the HHL outcome state when ancilla
qubit is measured in $\ket{0}$ and $\ket{1}$ and show condition for
postselection-free HHL running. We provide an explicit example of a
practically-interesting input matrix and an observable, which satisfy
postselection-free HHL condition. Our work can improve the performance of the
HHL-based algorithms.
