The two sides met each other in September in the Scottish Premiership, with David Martindale’s side coming away 1-0 winners in the end.
Fitzwater, who was on the pitch for the full 90 minutes on that occasion, feels that the margin of victory should have been more that time around.
He is taking heart from Livingston’s win, despite Celtic having won their last five games in a row, hitting top form under Ange Postecoglou.
“It was only a few weeks ago that we beat them so we will know what to expect”, Fitzwater was quoted as saying by the Daily Record.
“We’ll go there and be hard to beat. We defended well in numbers last time and made ourselves hard to beat.
“Even against United when we were down to 10 we created chances on the break.
“The game at home against Celtic we had arguably the better chances – we should have been two up by half-time.
“We will take the positives from that game and from Wednesday then go there with optimism
“It’s all about consistency, trusting the process and believing in what we are doing.”
Livingston are currently placed ninth in the league table, leading relegation-threatened Dundee by four points.
Celtic have found success hard to come by against Livingston of late, having won just one of their last four meetings, drawing two.
