。
He wrote it down so he wouldn't forget.
Literal
Forget-not [so-that-ように] he [topic-は] that [object-を] noted-down.
The ~ないように + 書き留めた frame ('wrote down so as not to forget') is the standard Japanese way to express the purpose of a note. Here the subject 彼 is explicit and topicalized with は — useful contrast against versions where the subject is dropped entirely, since Japanese can swing freely between explicit and elided subjects depending on what the surrounding discourse already supplies.