[ by Melanie Gretchen ] The SEC is looking to reduce the huge influence that high-frequency traders have on stock trading, and one option would be to charge fees for the myriad of buy and sell orders that are subsequently are canceled.  This consideration is supported by SEC Chairman Mary Schapiro, who is troubled and worried by the state of trading. She notes that a large portion of equities trading has little to do with "the fundamentals of the company that's being traded."  Instead, market volume is driven by the "minuscule aberrational price move" that computer-assisted traders, with direct connections to the exchange, can "jump on" in fractions of a second. Such activity "worries me," Ms. Schapiro to a breakfast meeting attended by reporters. That's when she mentioned the idea of curbing high-frequency traders forcing them to pay for the canceled trades that make up 9/10's of all orders. Of course, the SEC has other possible remedies in mind - like requiring such traders to maintain competitive buy and sell orders in the market throughout most of the trading day.   The Agency also would consider implementation of obligations for certain high-frequency traders to provide quotes near the NBBO during a certain percentage of the trading day. The Trump Card: Liquidity. Whenever the regulators talk about shortening the leash on HFT, the computer-trading industry warns that market liquidity could be the victim.  That could happen, they say, if regulators impose new fees or limits on rapid trades, potentially altering the market's landscape.  "It's going to chase a key constituency away" from the stock market, with some closing shop and others moving overseas, said Adam Honoré, research director at Aite Group, which follows computer trading. While worries about HST have been expressed at the SEC and the CFTC for years, Ms. Schapiro's current remarks indicate a heightened sense of concern that suggest aggressive action may be looming.  And, in all fairness to the SEC, Ms. Schapiro acknowledged that HFT's provide liquidity to markets, "and that's a great thing.  It's lowered the cost of trading." But that advantage does not offset some of her concerns, which caused the Flash Crash of May 6, 2010, when the DJIA plunged hundreds of points in a matter of minutes before recovering much of the lost ground.  An SEC report after the crash found that many high-frequency firms stopped trading during the upheaval, and some placed added pressure on the market by selling their positions. Many executives in charge of brokerage firms told Ms. Schapiro in the months after the crash that retail investors were "on the sidelines" until they understood what happened that day, she said Wednesday. For further details, go to  [WSJournal, 2/23/12].