Lineen told www.glasgowwarriors.org: "As with our other recent draws on the road at Dragons and Montpellier, it's indicative of the standards we've set ourselves that we came away from Murrayfield feeling unsatisfied.
"Yet again the players showed great character and spirit to claw their way back into the match, but we're all very keen to stop putting ourselves in positions where we need to do that.
"We really want to assert our own game and ensure it's the opposition that are scrambling to stay in contention. Key to that is starting better than we have in the last few matches, and we've spoken on the topic this week.
"As a coaching team, we've been delighted with the way the guys have been hanging tough and found a way to achieve what have been very respectable results on our travels of late. What we're really excited to see is how much more we're capable of if we play on the front foot from the start and bring our attacking threats into the game more consistently."
The Warriors starting line-up for the game bears seven changes from the deadlock at the national stadium. Two of these switches are injury-enforced, Jon Welsh replacing Ryan Grant (ankle) at loose-head prop, and Colin Shaw taking the wing berth vacated by Rory Lamont.
The 26-cap back-three man suffered a blow to the head/face during the first game, and was taken to hospital for a precautionary scan. He was discharged later that night, and has since been subject to further assessment from the Warriors medical team. The medics are happy with Lamont's progress, but he has not been deemed ready to play this weekend.
The majority of the other changes come in the pack, where Dougie Hall and Moray Low form an all-new front row with Welsh, Ryan Wilson starts at No.8, and Chris Fusaro occupies the openside flanker berth, John Barclay moving to the bench.
In the backs, meanwhile, Peter Murchie replaces Troy Nathan and will start at full-back, with Stuart Hogg moving to outside centre.
Lineen commented: "We've freshened things up in the forwards, bringing in guys who have performed well as replacements in recent weeks and have really put their hand up for a start.
"Moray and Dougie bring excellent experience and class to our pack, while Chris Fusaro has been very consistent all season.
"It's great for quality players like John Barclay to have that level of competition, and having his game knowledge and ability to call on from the bench is a real asset for us this weekend.
"We sustained a couple of injuries in the first game, so we've had to shuffle things a bit, but we're more than happy with the quality of the replacements that are coming into the side.
"Jon Welsh is a proven competitor in the front row, while Colin Shaw was first class off the bench at Murrayfield, showing good awareness for his try.
"Ryan Wilson has had an excellent campaign to date, Peter Murchie is a player we rate very highly, and we're also very excited about what Stuart Hogg can bring to the outside centre position.
"Sunday is about us coming sharply out of the blocks, hitting the ground running and playing the game on our terms. It's going to be another massively physical battle, so we'll need to be right at the top of our game if we're going to keep hold of the silverware."
One of the oldest fixtures in world sport, the Glasgow v Edinburgh clash celebrates 140 years of history in 2012.
Fans can get in the mood for the historic New Year's Day clash by taking part in the club's pre-match party in George Square.
Hosted in conjunction with Glasgow Life and Clyde 1, there will be music, player signing/photo sessions and a fully licensed bar. The party will take place in the Winter Café Bar, beside the 'Glasgow on Ice' rink.
Ticket sales for Sunday's winner takes all clash are selling fast, with just over 1,500 remaining. Supporters wishing to attend the game were today urged to act fast to avoid disappointment.
Fans are also advised that there will be increased demand for on-street parking in the vicinity of Firhill on Sunday, and are encouraged to car share where possible. Supporters who wish to offer or request lifts to/from other supporters can do so via Twitter, using #1872carshare.
Everyone is encouraged to arrive as early as possible, particularly those requiring to collect tickets.
Tickets are available via www.glasgowwarriors.org, by calling 0844 800 3490 or in person at the Glasgow on Ice box office on George Square and the Gordon Street and Sauchiehall Street branches of Greaves Sports, our official retail partner.
GLASGOW WARRIORS TEAM TO PLAY EDINBURGH RUGBY IN THE RABODIRECT PRO12 AT FIRHILL ON SUNDAY 1 JANUARY 2012 (KICK-OFF 5.35PM, LIVE ON BBC ALBA)
15 Peter Murchie
14 David Lemi
13 Stuart Hogg
12 Graeme Morrison
11 Colin Shaw
10 Duncan Weir
9 Chris Cusiter
1 Jon Welsh
2 Dougie Hall
3 Moray Low
4 Richie Gray
5 Al Kellock (captain)
6 Rob Harley
7 Chris Fusaro
8 Ryan Wilson
SUBSTITUTES
16 Pat MacArthur
17 Mike Cusack
18 Ed Kalman
19 Tom Ryder
20 John Barclay
21 Henry Pyrgos
22 Troy Nathan
23 Ruaridh Jackson
Not considered for selection due to injury: Federico Aramburu (shoulder), Ryan Grant (ankle), Rory Lamont (head/face), DTH van der Merwe (shoulder).
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