The curved screen is a feature provided to a quick way to stay in touch with select contacts, and to alert owners to important information.
Galaxy S6 Edge with curved screen unveiled at Mobile World Congress
The new Samsung phones were unveiled in Barcelona, ahead of the start of and go on sale Friday, April 10 in 20 countries.
It will be sold for a higher price than the standard S6, which otherwise has the same specifications.
Changes include making the TouchWiz user interface simpler to use by cutting the number of pop-up messages and introducing a metal frame and glass back instead of the plastic styling of earlier models.
The Galaxy S6 is not water-resistant, they do not have a microSD slot for extra storage and their backs cannot be removed to change their batteries.
The S6 phone's front camera has been upgraded to five megapixels, while the rear one stays at 16MP.
Samsung has also taken steps to make the camera quicker to use, saying it now takes less than a second to double tap the home key and snap a shot.
Samsung looks to have beaten Apple to be the first to embed support for both the PMA and WPC's Qi wireless charging standards.
The Android-powered handsets are also faster to recharge, and should return to 50% battery strength within half an hour of being plugged in.
Other improvements over the S5 include; Increased screen resolution - now 577 pixels per inch - and the ability to go 20% brighter, a new 14 nanometre processor designed by Samsung, rather than bought from Qualcomm, that should be more energy efficient.
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