  A new class of semi-implicit numerical schemes for linear advection equation
on Cartesian grids is derived that is inspired by so-called $\kappa$-schemes
used with fully explicit discretizations for this type of problems. Opposite to
fully explicit $\kappa$-scheme the semi-implicit variant is unconditionally
stable in one-dimensional case and it preserves second order accuracy for
dimension by dimension extension in higher dimensional cases. We discuss von
Neumann stability conditions numerically for all numerical schemes. Using
so-called Corner Transport Upwind extension of two-dimensional semi-implicit
scheme with a special choice of $\kappa$ parameters, a second order accurate
method is obtained for which numerical unconditional stability can be shown for
variable velocity and the third order accuracy can be proved for constant
velocity. Several numerical experiments illustrate the properties of
semi-implicit schemes for chosen examples.
