The modified conjugation law for fermion fields is suggested providing Hermiticity of the de Sitter supergravity action with the positive cosmological constant lambda >0. It is shown however that the modified conjugation leads to an indefinite metric Hilbert space, i.e. although de Sitter supergravity exists, it possesses ghosts. The corresponding N=1 supersymmetric de Sitter algebra is constructed. It is found that this algebra is not an ordinary Lie superalgebra but belongs to the class of generalised (Z₂*Z₂-graded) Lie superalgebras.