Right click and select remove taskbar icon. Did you try that.

I don't have that option in the context menu of the desktop shortcut or the taskbar icon itself. There is only "Unpin from taskbar" option but it doesn't do anything other than removing the pinned, fixed icon in the taskbar. When I click "Pin to taskbar" after that, the problem occurs again.

King Massen, I think you may have encountered a glitch when installing / pinning previously, as I think the generally expected behaviour for pinned apps is that a new window is launched only if the app wasn't already running, else the pre-existing window is shown instead.

Sorry I can only offer vaguish suggestions here.

Is there a "New Window" button that you could pin to the toolbar within Firefox, taken from the 'Customise Toolbar'"page? If so, would clicking on that rather than the taskbar icon be a workaround?

However if you really want the pinned icon to always launch a new window, and not use buttons within the Firefox interface itself for this, then some things you could try:

Close Firefox and then unpin it. Find the Firefox executable on your hardrive (for example, "C:\Program Files\Mozilla Firefox\firefox.exe") and try pinning it directly, via its right-click menu.

If that doesn't work, find a pre-existing Firefox shortcut on your Start screen or menu and copy it to somewhere else on your system (or create a new shortcut to Firefox yourself). Then modify it so that it now has the -new-window command-line option to always open a new window. If you are unsure how to modify your shortcut to add this command-line option see the chosen solution here: https://support.mozilla.org/en-US/questions/1287367 Then pin your newly modified shortcut to the taskbar and see if that does what you want.