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The phrase "a new method and" is correct and usable in written English.
It can be used when introducing a new approach or technique, often in a list or comparison context.
Example: "The research presents a new method and several innovative techniques for data analysis."
Alternatives: "an innovative approach and" or "a fresh technique and".
Exact(55)
In short, Wilson called for "a new method and spirit of counsel" to replace politics-as-usual in Washington.
In 1884 Hertz derived Maxwell's theory by a new method and put its fundamental equations into their present-day form.
"I suppose for us it was going with a new method and a new group of players," replied the 29-year-old, politely, when asked how his national team recovered from its Iceland moment.
Biotechnology companies were once known for going boldly where the big pharmaceutical companies would not, developing genetically engineered medicines like Avastin, the Genentech drug, approved on Thursday, that attacks cancer by a new method and prolongs the lives of patients.
Liverpool were dire in the first third of the season as Brendan Rodgers grappled for a new method and then, just as it seemed they had got their act together and could challenge for a return to the Champions League (in which they were terrible this term), they fell apart again, leading to suggestions that they need more major surgery in the summer.
A new method and algorithm based on ZXCOM was used.
Similar(5)
In addition Yoshimura et al. [ 57] describe a new methods and new technologies in the use of fat grafting.
A new method for diagnostics and reduction of dynamical systems and chemical kinetic models is proposed.
This paper presents a new method which extracts and selects features from multi-channel EEG signals.
This research provides a new method of power and data transmission for underwater sensor nodes.
In this paper we propose a new method for sharpening and refinements of some trigonometric inequalities.
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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