* Banking sector gets ECB liquidity injection
* German two-year yields could dip negative, say strategists
* Analysts see slow healing process in money markets
(Adds fresh quotes, updates prices)
LONDON, June 17 (Reuters) - German two-year bond yields traded near one-year lows on Tuesday, as the European Central Bank released tens of billions of euros into the euro zone banking sector, anchoring short-term interest rates around zero.
For the first time the ECB did not hold a weekly deposit tender to neutralise the effect of the bond purchases it made at the height of the crisis, effectively injecting back into the market the 108 billion it drained last week.
That was partly offset by banks taking less in one-week loans than last Tuesday at the ECB's regular offering of unlimited cash - 98 billion euros compared with 137 billion - but still represented a significant cash injection.
German two-year bond yields edged 2 basis points higher on the day to 0.047 percent, but were still close to the 0.027 percent hit on Monday, which was the lowest since the end of May 2013.
Shorter-dated bonds outperformed in a broader sell-off on Tuesday, which traders said was driven by fears the U.S. Federal Reserve may raise interest rates sooner than expected after consumer prices made their largest jump in more than a year.
Some analysts said that the ECB's liquidity injection could push two-year yields into negative territory, adding however that it would be only a temporary phenomenon as investors would eventually sell two-year bonds for longer-dated debt or paper from other issuers to get a positive return.
"The boost to excess liquidity in the system will compress rates but we are not really looking for significant negative yields," said Anton Heese, co-head of European interest rates strategy at Morgan Stanley.
"In the past when you have seen negative yields, it has been driven more by a safe haven bid rather than excess liquidity."
Germany and the Netherlands sold treasury bills at a negative yield on Monday, the direct result of the ECB cutting the rate it offers banks to keep their money in overnight deposits to minus 10 basis points.
The ECB's move is effectively penalising banks for not putting money to work. Negative T-bill yields mean governments will pay investors back less than they borrowed when the paper comes due.
Policymakers hope negative rates in time will force money out of the financial system and into the real economy. But some analysts remain pessimistic.
"If you don't want to lend money to businesses because you don't trust the economic viability of companies, you will not do it, no matter what incentives you get from the central bank," said Marius Daheim, chief strategist at Bayerische Landesbank.
"The credit channel is blocked ... People don't trust the economy because growth is feeble, inflation is low, household debt is pretty high and unemployment is high as well."
The fact that banks reduced their take-up by 40 billion euros just as the ECB injected nearly three times that sum in the market shows the bloc's banking system remains fragmented.
It means the ECB's cash withdrawals had mainly been funded by the higher-rated banks in the euro zone's healthier states, while lower-rated peripheral banks remain reliant on ECB liquidity. At the same time, money fails to flow smoothly from the core banks to the peripheral banks.
Negative deposit rates might in the future help reduce fragmentation, in a process that will lead to smaller ECB liquidity injections, shrinking the banking sector's spare cash and keeping money market rates positive.
"Some banks, maybe a small percentage, may decide to lend a bit more to the periphery. But we're talking about months, quarters, maybe a year," said Elwin de Groot, market economist at Rabobank.
(Additional reporting by John Geddie; Editing by Nigel Stephenson and Mark Trevelyan)