"fourth consecutive month" is correct and can be used in written English.
It can be used to indicate that something has been happening for four months in a row. For example: "Company profits have been rising for the fourth consecutive month."
The economy's index of leading indicators rose for a fourth consecutive month in July (though it remains to be seen whether this momentum can be carried into August).
Investor confidence in Germany rose for a fourth consecutive month in February, and by more than expected.Japanese finance minister Shoichi Nakagawa has quit his post.
Germany's IFO institute's closely watched index of business confidence (based on the views of 7,000 companies) rose for a fourth consecutive month in February.
The University of Michigan consumer-sentiment index fell for the fourth consecutive month in September, though less dramatically than many expected.
Eurozone retail sales rose for a fourth consecutive month in January, official statistics have shown, indicating the zone's economy may be picking up.
According to the Federal Aviation Administration, business jet flight activity was up 18.12 percent from a year earlier in March, the fourth consecutive month to show a rise.
A reading above 50 indicates growth, and April was the fourth consecutive month of growth.
The Conference Board's index of leading economic indicators fell in September for the fourth consecutive month.
The Standard & Poor's 500-stock index still managed to close out February with a fourth consecutive month of gains.
The headline numbers are pretty decent; both the 10-city and 20-city indexes saw month-over-month price increases in September for a fourth consecutive month.
The Consumer Confidence Index fell in January for the fourth consecutive month.
