Martin,
While it is possible it could be a CS naval pennant or it might just be a different type of patriotic US banner. The link below will show a scan that came from a turn of the 20th century Dettra flag catalog with various types of banners (see lower right corner for stars & bars type). There are 2 more pages of just different types banners but no mention of any being Confederate. I see yours is more of a pennant than a regular banner but maybe it is just a patriotic pennant with no Confederate connections. The pennant shown in Madaus' book Rebel Flags Afloat is smaller, narrower and have all the stars in a straight line (as too the custom with US naval pennants).