nonetymological

The story

1. Proto-Indo-European*né
2. Proto-Germanic*ne
3. Proto-Indo-European*ís?
4. Proto-Indo-European*h₁óynos
5. Proto-Germanic*ainaz
6. Proto-Germanic*nainaz
7. Proto-West Germanic*nain
8. Old Englishnān
9. Middle Englishnon
10. Old Englishnān
11. Old Englishnān-
12. Middle Englishnon-
13. Englishnon-
14. Proto-Indo-European*set-?
15. Ancient Greekἐτεός (eteós)der.?
16. Ancient Greekἔτυμος (étumos)
17. Proto-Indo-European*leǵ-
18. Proto-Indo-European*lóǵos
19. Proto-Hellenic*lógos
20. Ancient Greekλόγος (lógos)
21. Ancient Greekἐτῠμόλογος (etŭmólogos)
22. Ancient Greekἐτῠμολογῐ́ᾱ (etŭmologĭ́ā)
23. Latinetymologia
24. Old Frenchethimologie
25. Middle Englishethymologie
26. Englishetymology
27. Proto-Indo-European*h₂el-
28. Proto-Indo-European*h₂élisder.?
29. Englishetymological
30. English todaynonetymological

From non- + etymological.