In this paper, we introduce the concept of $D$-direction curve and $C$-direction curve of a given curve using the alternative frame {${N,C,W}$} in Euclidean 3-space. Furthermore, we define a $(N,C)$ plane curve, a $(N,W)$ plane curve and a $(C,W)$ plane curve of a given curve, and give some results related to them. Finally, we present some illustrated examples for new associated curves.