Drawing new image over old image java

I need to draw a new image over old image. I first opened both images in BufferedImage and changed their white background to transparent. Then I got a Graphics2D object from the bufferedImage of old image and called drawImage method of Graphics2D class. I then saved the old image to disk. When I open the saved image I find only the old image with white background changed to transparent. Can anyone suggest me what is error with my code or how can I get to fix my error ?

    BufferedImage newImage = ImageIO.read(new File("new.png"));
    BufferedImage oldImage = ImageIO.read(new File("old.png"));

    newImage = makeWhiteTransparent(oldImage);
    oldImage = makeWhiteTransparent(newImage);

    Graphics2D graphics = (Graphics2D) oldImage.getGraphics();
    graphics.drawImage(newImage,null, 0,0);

    File outputImage = new File("merged.png");
    ImageIO.write(oldImage, "png", outputImage);