  Let $P$ and $Q$ be idempotents on a Hilbert space $\mathcal{H}.$ The minus
order $P\preceq Q$ is defined by the equation $PQ=QP=P.$ In this note,
  we first present some necessary and sufficient conditions for which the
supremum and infimum of idempotents $P$ and $Q$ exist with respect to the minus
order. Also, some properties of the minimum $Q^{or}$ are characterized, where
$Q^{or}$=min $\{P^{'}: P^{'}$ is an orthogonal projection on $\mathcal{H}$ with
$Q \preceq P^{'} \}.$
