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The phrase 'but the new method' is correct and usable in written English.
You can use it when you are contrasting two ideas; for example, "The old method proved inefficient, but the new method has been successful."
Exact(9)
But the new method is a work in progress.
But the new method, reported yesterday by researchers at Advanced Cell Technology on the Web site of the journal Nature, had little immediate effect on longstanding objections of the White House and some Congressional leaders yesterday.
Past experiments usually analyzed a sample for one target component, like ginseng or rhino horn, but the new method approaches the medicine holistically to see what plants, animals, insects or fish might be present.
Normally, influenza vaccines are made by culturing live virus in hens' eggs, a risky and time-consuming procedure, but the new method was simpler and it produced a vaccine that appears to generate immunity to a wide range of flu viruses rather than being restricted to just one strain, scientists said.
Testing to check for horse meat is generally done using DNA analysis, but the new method allows for a simpler and quicker test that can be performed onsite.
But, the new method can be applied in different cities and in different heat source distributions, and can achieve a considerably high energy saving rate, ranging from 5.2% to 21.4%.
Similar(47)
But with the new method, human cloning for stem cell research, like the creation of human embryos to extract stem cells, may be unnecessary.
It adopts the economic classification system shared by the United States and Canada, breaking the economy down into 750 different activities, rather than 362 as before.But even the new method may underestimate Mexico's output.
But under the new method of counting, Ithaca is considered to have only 9 commercial stations, and any single company can own no more than 5. Though the F.C.C. is not requiring radio companies to give up any stations they already own, the companies say the tighter limits will make it hard to continue expanding to achieve the economies of scale they see as necessary to be profitable.
Both approximate methods produce the same relaxation rate as DSMC, but only the new method produces a nonequilibrium distribution function similar to that for DSMC.
But with the new method in place for OS X Lion, Apple had developers log in and get a special redemption code that they were told to use in the Mac App Store to get OS X Lion.
More suggestions(16)
but the exact method
but the new centralisation
but the new aid
but the new Bond
but the scientific method
but the new study
but the new regime
but the new direction
but the new arena
but the new defence
but the same method
but the new work
but the new restoration
but the chic method
but the new strategy
but the proposed method
Write better and faster with AI suggestions while staying true to your unique style.
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