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The phrase "according to a documented method" is correct and usable in written English.
You can use it when referring to a specific procedure or approach that has been formally recorded or established.
Example: "The experiment was conducted according to a documented method to ensure accuracy and reliability in the results."
Alternatives: "following a recorded procedure" or "in line with an established method."
Exact(1)
The genomic DNA of every generation was extracted from the 4-day-old colonies according to a documented method (Raeder and Rroda 1985) and used as PCR templates to detect the AaIT gene presence in the recombinants with SP-AaIT-F and SP-AaIT-R primers (5′-CCCAAGCTTATGCGTGAACTTTCTTCGGT-3′ and 5′-CCCTCGAGTTAGTTGATGATGGTGGTAT-3′, respectively).
Similar(59)
The resulting reports are reviewed internally according to a documented quality control and assurance protocol.
The latest BP-related outrage (we could use an index) is that the company, according to a document obtained by the Times, was given the choice between two casing methods for the well.
Here are the facts, according to a document on the court's Web site.
The saponin contents in the crude extract were determined according to documented method [ 8].
Recruitment curves for each coil were measured according to a previously documented procedure [24 26].
The total cost was $277,461, according to a university document.
(According to a C.I.A. document, it was supposed to help "clear a person's head").
She later found a job at Man Financial, according to a court document.
One of his victims, according to a government document, was a Manhattan doctor named Eli Sckolnick.
Bite marks were discovered all over the woman, according to a court document.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com