Hilbert $C^{*}$-modules with complementing property

We give the characterization and description of all full Hilbert $C^*$-modules and associated $C^*$-algebras having the property that each relatively strictly closed submodule is orthogonally complemented. A strict topology is determined by essential ideal in the associated algebra and related ideal submodule. It is shown that these are some modules over hereditary $C^*$-algebras containing the essential ideal isomorphic to algebra of (not necessarily all) compact operators on a Hilbert space. The characterization and description of that broader class of Hilbert modules and associated $C^*$-algebras is given.