Aberdeen have still to score against Dundee at Pittodrie under Ebbe Skovdahl, after this fifth attempt to do so ended in stalemate.
Indeed, in their last six games at home to Ivano Bonetti's side, the Dons haven't won once and it's now more than five years since their last success over the Taysiders, a 1-0 victory in the Scottish League Cup.
It wasn't for want of not trying though, as they pounded their guests' goal in a second-half onslaught after Dundee had done the same to them in the first 45 minutes, only to be greeted by a chorus of boos from the home fans on the final whistle.
Dundee had the first chance to open the scoring after just 20 seconds, when Georgian international Temuri Ketsbaia played the ball through to Steven Milne but he knocked it to far on and keeper Peter Kjaer blocked with his legs.
Within 30 seconds, the away side had surged forward again as they looked to snatch an early lead and Frenchman Khaled Kemas - a former PSG team-mate of Nicolas Anelka - passed to Milne but once again he saw his effort blocked by
Danish keeper Kjaer.
Aberdeen's first chance of the game came after eight minutes when Robbie Winters - the Dons top scorer with 12 goals this season - just failed to connect with Kevin McNaughton's pinpoint cross from the right from just six yards out.
Dundee were having the better of the opening exchanges though and on 13 minutes they should have gone ahead.
Milne broke clear with the ball down the right and released Kemas but after he cut inside he could only shoot into the side-netting.
Aberdeen were struggling to break down the well-organised away defence and couldn't muster any real attempts on goal, with wayward crosses and overhit passes coming closest to troubling keeper Julian Speroni.
And while their defending was stout, Dundee's attacking continued to be equally industrious, with Enrique 'Kiko' Torres coming close to giving them a deserved lead after 34 minutes.
Milne laid the ball to David MacKay and his low cross from the right wing was met by the former Numancia man but he fired well over from the edge of the penalty area
The home side's best attempt on goal of the half came four minutes later through Winters, whose quick free kick was played back to him by Darren Young before he fired a low shot goalward but even that didn't trouble Speroni and it remained goalless at the interval when Dundee should have led.
Skovdahl threw on Darren Mackie for the ineffective Eugine Dadi at the start of the second half and the home side charged forward in a bid to claim an early lead but once again Bonetti's men stood firm in defence, with Winters and Derek Young having efforts blocked.
But on 50 minutes they almost made a breakthrough. Fergus Tiernan hit a firm shot from the right of the area and after making a good save, Argentinian keeper Speroni made a spectacular dive to palm the ball away from the incoming Winters.
Aberdeen continued to push forward, and after McAllister had seen his powerful 30-yard strike deflected wide, Derek Young headed Winters' left-wing corner three yards over the upright before Tiernan fired wide on the hour mark.
On 63 minutes, Dundee made a second change as Aberdeen threatened to overrun them, with Milne coming off after an impressive first period to be replaced by Alessandro Romano but it made no difference and Skovdahl's men continued to
press ahead.
They should have gone in front on 65 minutes when Winters picked out Cato Guntveit with his deep cross from the left, but the Norweigian only got a glancing touch on the ball and it ran across the face of Speroni's goal and
wide.
Dundee hit back immediately, and Gavin Rae broke clear of the Dons defence but was stopped by a superb sliding tackle by McAllister on the edge of the box, and the ball was cleared.
But that attempt brought just a brief break from the incessant Reds pressure and Winters put another header wide of the post on 71 minutes following an excellent cross from McNaughton on the right.
Dundee looked to be settling for a draw as they seldom ventured further than the halfway line but could have snatched a win with six minutes remaining when Rae surged forward with the ball after being fed by Beith and he set up Ketsbaia but the former Newcastle hitman's shot from 18 yards sailed high over the crossbar.
Teams
Aberdeen (0) 0 Dundee (0) 0
Aberdeen: Kjaer, McNaughton, McGuire, Whyte, McAllister,
Guntveit, Darren Young, Tiernan, Winters, Derek Young,
Dadi (Mackie 46).
Subs Not Used: Esson, Solberg, Thornley, Clark.
Dundee: Speroni, Smith, Zhiyi, Del Rio, Beghetto (Beith 70),
MacKay, Ketsbaia, Rae, Torres, Milne (Romano 63),
Kemes (Caballero 54).
Subs Not Used: Langfield, Garrido.
Booked: Ketsbaia.
Att: 10,127
Ref: D McDonald (Scotland).