A densely defined closed linear operator \(F\) in a Hilbert space is said to be idempotent if \(\text{ran}(F)\subset \text{dom}(F)\) and \(F\cdot F = F\). The author shows that such an idempotent operator can be written as \(F = P(P + Q )^{-1/2} \cdot (P + Q )^{-1/2}\), where \(P\) and \(Q\) are the orthoprojections onto \(\text{ran}(F)\) and \(\ker(F)\), respectively. It is known that a densely defined closed linear operator \(F\) is bounded if and only if \(\text{dom}(F)=H\). The author then shows that if the idempotent \(F\) is bounded, then for any \(\lambda\neq 0\) the operator \(P+\lambda Q\) is invertible and \(F=P(P+\lambda Q)^{-1}\), \((P+\lambda Q)^{-1}=(P+Q)^{-1}(P+\lambda^{-1}Q)(P+Q)^{-1}\) and \(\|F\|=\|(P+Q)^{-1}\|\).