One way would be to select the white with the magic wand tool, select inverse, right click inside the selection and choose Layer via Copy.
Then go to Enhance>Adjust color>Defringe Layer with a setting of 1 pixel.
You would have to either delete the background layer and save as a psd,png or tiff (formats that support transparency)
or turn off the visibily of the background layer and use File>Save for Web and choose png-24 with the Transparency box checked.
Europe, Middle East and Africa