The evolute and involute curves, Mannheim curves or Bertrand curves are thefamous examples of the associated curve pairs. In the view of suchinformation we have defined $ NP^{\ast }$ curve pairs where the principalnormal vector of the first curve and the vector $P^{\ast }$ lying on thenormal plane of the second curve are linearly dependent. We have calledthese curve pairs $NP^{\ast }-$ curves. Second curve is named $NP^{\ast }-$partner curve. Also, while the examination of $NP^{\ast }-$ curves we obtainsome relations for the curvatures and Frenet apparatus of the second curvebased on the Frenet apparatus of the first curve.