No, it's not valid to do so since according to the Mattel's UNO rules the next player forfeit their turn and MUST draw 4 cards from the pile.
But for the player after the next player (who had to pick up the 4 cards) it's a valid play.
Anything else is just house rules...
From mattel.com: https://service.mattel.com/instruction_sheets/42001pr.pdf
Wild Draw 4 Card - This card allows you to call the next color played and requires the next player to pick 4 cards from the DRAW pile and FORFEIT his/her turn.
Note: The player in turn (after the player who had to draw 4 cards) may play a Wild Draw 4 Card with consideration to the color chosen by the player playing the first Wild Draw 4 Card.
So in that case you could say that a Wild Draw 4 Card could be played on a Wild Draw 4 Card.
Remember that it's only the next player who can make the challenge.
Wild Draw 4 Card - ... Only the person required to draw the 4 cards can make the challenge.