how to round_corner a logo without white background(transparent?) on it using pil?

I got a square logo and I need to round_corner it, searched for a while and got the follow code "working":

def round_corner_jpg(image, radius):
    """generate round corner for image"""
    mask = Image.new('RGB', image.size)
    #mask = Image.new('RGB', (image.size[0] - radius, image.size[1] - radius))
    #mask = Image.new('L', image.size, 255)
    draw = aggdraw.Draw(mask)
    brush = aggdraw.Brush('black')
    width, height = mask.size
    draw.rectangle((0,0,width,height), aggdraw.Brush('white'))
    #upper-left corner
    draw.pieslice((0,0,radius*2, radius*2), 90, 180, None, brush)
    #upper-right corner
    draw.pieslice((width - radius*2, 0, width, radius*2), 0, 90, None, brush)
    #bottom-left corner
    draw.pieslice((0, height - radius * 2, radius*2, height),180, 270, None, brush)
    #bottom-right corner
    draw.pieslice((width - radius * 2, height - radius * 2, width, height), 270, 360, None, brush)
    #center rectangle
    draw.rectangle((radius, radius, width - radius, height - radius), brush)
    #four edge rectangle
    draw.rectangle((radius, 0, width - radius, radius), brush)
    draw.rectangle((0, radius, radius, height-radius), brush)
    draw.rectangle((radius, height-radius, width-radius, height), brush)
    draw.rectangle((width-radius, radius, width, height-radius), brush)
    draw.flush()
    del draw
    return ImageChops.add(mask, image)

then I saved the returned image object,however it has white background in the corner like this How can i get rid of the white background or make it invisible? Thanks in advance~

EDIT: here is the code by fraxel,thanks~

def add_corners(im, rad):
    circle = Image.new('L', (rad * 2, rad * 2), 0)
    draw = ImageDraw.Draw(circle)
    draw.ellipse((0, 0, rad * 2, rad * 2), fill=255)
    alpha = Image.new('L', im.size, "white")
    w, h = im.size
    alpha.paste(circle.crop((0, 0, rad, rad)), (0, 0))
    alpha.paste(circle.crop((0, rad, rad, rad * 2)), (0, h - rad))
    alpha.paste(circle.crop((rad, 0, rad * 2, rad)), (w - rad, 0))
    alpha.paste(circle.crop((rad, rad, rad * 2, rad * 2)), (w - rad, h - rad))
    im.putalpha(alpha)
    return im


if __name__ == '__main__':
    im = Image.open('1.jpg')
    im = add_corners(im, 100)
    im.save('out.png')`

I am so sorry..I need the image shape to be ellipse not rectangle,I.E. the write stuff off the pic,and @fraxel, I still can see the white corner in the pic you processed for me

First off, make sure you are saving your image in a format that supports transparency. PNG does, JPG does not... Below is some pretty nice code that will add transparent corners. It works like this:

1. Draws a circle with radius, rad, using draw.ellipse()
2. Create an image for the alpha channel the same size as your image
3. Chop our circle into four pieces (the rounded corners), and place them in the correct corners of the alpha image
4. Put the alpha channel into your image using putalpha()
5. Save as a png, thus preserving transparency.

Here is the code:

import Image, ImageDraw

def add_corners(im, rad):
    circle = Image.new('L', (rad * 2, rad * 2), 0)
    draw = ImageDraw.Draw(circle)
    draw.ellipse((0, 0, rad * 2 - 1, rad * 2 - 1), fill=255)
    alpha = Image.new('L', im.size, 255)
    w, h = im.size
    alpha.paste(circle.crop((0, 0, rad, rad)), (0, 0))
    alpha.paste(circle.crop((0, rad, rad, rad * 2)), (0, h - rad))
    alpha.paste(circle.crop((rad, 0, rad * 2, rad)), (w - rad, 0))
    alpha.paste(circle.crop((rad, rad, rad * 2, rad * 2)), (w - rad, h - rad))
    im.putalpha(alpha)
    return im

im = Image.open('tiger.jpg')
im = add_corners(im, 100)
im.save('tiger.png')

example curved edge tiger:

here is your image, processed with this code, giving transparent corners: