There is a thread on ubuntuforums dedicated to resolving this. Below I've just summarised the thread - note - apparently this 'fix' depends on the theme you are using. Looking through the thread from back-to-front, there is an alternative suggested answer involving compiling code. If below doesnt work for you have a look at the thread to see if the compile option works.
gedit ~/.gtkrc-2.0
replace the contents with the following (n.b. if there is a blank file you are probably not using a standard theme so this probably will not work)
style "panel-arrow-remove"
#the following removes the arrows from the panel
{
engine "pixmap"
{
image
{
function = ARROW
recolorable = TRUE
overlay_file = "arrows/arrow-blank.png"
overlay_border = {2,2,2,2}
overlay_stretch = FALSE
arrow_direction = UP
}
image
{
function = ARROW
recolorable = TRUE
overlay_file = "arrows/arrow-blank.png"
overlay_border = {2,2,2,2}
overlay_stretch = FALSE
arrow_direction = DOWN
}
image
{
function = HANDLE
recolorable = TRUE
overlay_file = "arrows/arrow-blank.png"
overlay_stretch = FALSE
orientation = VERTICAL
}
image
{
function = HANDLE
overlay_file = "arrows/arrow-blank.png"
overlay_stretch = FALSE
orientation = HORIZONTAL
}
}
}
widget_class "*PanelToplevel*" style "panel-arrow-remove"
Save, reboot.