‎We investigate the orthogonality preserving property for pairs of operators on inner product‎ ‎$C^*$-modules‎. ‎Employing the fact that the $C^*$-valued inner product structure of a Hilbert‎ ‎$C^*$-module is determined essentially by the module structure and by the orthogonality structure‎, ‎pairs of linear and local orthogonality-preserving operators are investigated‎, ‎not a priori bounded‎. ‎We obtain that if $\\\\mathscr{A}$ is a $C^{*}$-algebra‎ ‎and $T‎, ‎S:\\\\mathscr{E}\\\\to \\\\mathscr{F}$ are two‎ ‎bounded ${\\\\mathscr A}$-linear operators between full Hilbert‎ ‎$\\\\mathscr{A}$-modules‎, ‎then $\\\\langle x‎, ‎y\\\\rangle = 0$ implies $\\\\langle T(x)‎, ‎S(y)\\\\rangle = 0$‎ ‎for all $x‎, ‎y\\\\in \\\\mathscr{E}$ if and only if there exists an element $\\\\gamma$‎ ‎of the center $Z(M({\\\\mathscr A}))$ of the multiplier algebra $M({\\\\mathscr A})$‎ ‎of ${\\\\mathscr A}$ such that $\\\\langle T(x)‎, ‎S(y)\\\\rangle = \\\\gamma \\\\langle x‎, ‎y\\\\rangle$‎ ‎for all $x‎, ‎y\\\\in \\\\mathscr{E}$‎. ‎Varying the conditions on the operators $T$ and $S$ we obtain‎ ‎further affirmative results for local operators and for pairs of a bounded and an unbounded‎ ‎${\\\\mathscr A}$-linear operator with bounded inverse‎.

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