Maybe it's a case of third time's the charm, or perhaps it's just consumer curiosity, but Microsoft's new Bing search engine has gained market share its second week in a row, according to net tracking firm comScore.

Microsoft (NASDAQ: MSFT) officially launched its Bing search engine on June 3, and briefly surged ahead of its closest competition Yahoo (NASDAQ: YHOO) that day, according to tracking firm StatCounter.

While Bing didn't stay in second place very long, though, it did pick up some market share during its first full week, according to figures calculated by tracking firm comScore, which tracks searches in the U.S.

Bing also picked up some market share -- albeit a small share -- during its second week of public usage, according to comScore data. "The results show that Microsoft has continued to increase its position in the search market following the initial week of Bing’s debut," said a statement released Wednesday by comScore.

In its first week, Bing increased Microsoft's search engine market penetration from 13.8 percent in a five day period in May to 15.5 percent in the period of June 2 through 6, an increase of 1.7 percentage points, according to comScore.

The gain during Bing's second week was smaller, though the graph keeps edging upward -- at least so far.

From June 8 through 12, Bing's market penetration grew another 0.9 percent to bring its share up to 16.7 percent.

Additionally, comScore says that Microsoft's share of search results pages has grown from 9.1 percent prior to the Bing launch, to 11.3 percent during its first week, to 12.1 percent during its second week of use -- a net gain of 3 percentage points in two weeks.

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Microsoft declined to comment for this story.