Neil Lennon expects his Celtic side to make amends for their defeat at Ibrox earlier in the season when Rangers visit on Wednesday night.
Celtic lost 4-2 in September's encounter but Rangers' 15 point lead racked up through November has now been reduced to one.
"We didn't do ourselves justice at Ibrox," said Lennon.
"So I am looking to my team to be highly motivated and play better and compete better," Lennon said.
A Georgios Samaras double in Saturday's 2-1 home win over Kilmarnock extended Celtic's winning run in the Scottish Premier League to eight games and took Lennon's side to within a point of Rangers at the top of the table, who lost 2-1 at St Mirren.
Lennon was not surprised by Rangers' defeat in Paisley but gave due respect to the Ibrox side, and, remembering the last encounter between the sides he was reluctant to speculate on how his Glasgow rivals would line up in Wednesday's match.
"I don't know how Rangers will approach the game," said Lennon, "Rangers manager Ally McCoist has tried a couple of different formations.
"He has played three up or one up. But, whatever formation we face on Wednesday, they are the champions and have had a good mentality over the last three or four years.
"But we are in a good place and I want us to go out and stamp our authority on the game if we can.
"I was not surprised at all (at Saturday's win for St Mirren). Anything can happen - particularly away from home.
"It has happened to us on a few occasions and St Mirren are a decent team at home - but I can't comment on Rangers.
"What I will say is that they are a point ahead and are current champions and our biggest rivals for the title and we will have to play very well to beat them.
"Yes, we have won eight in a row and the form is good, but we will have to play well, we will have to play strongly and have to play the occasion as best we can.
"We want to continue the winning form and if it means having to beat Rangers then so be it."
Left-back Emilio Izaguirre has now fully recovered from a broken ankle sustained against Aberdeen in August and was on the bench against Killie, while defender Kelvin Wilson came on in the second half following his recovery from an Achilles problem.
Lennon says both players have a chance of a starting place against Rangers.
"Izaguirre is in contention," said Lennon. "We wanted to give him some game time but when the Kilmarnock goal went in, we wanted to shore things up and make sure we didn't concede again.
"Kelvin Wilson is also definitely in contention.
"He was unlucky not to start against Kilmarnock."