How to create a line graph which ignores zero values

I want to create a graph showing trends over time, calculated from a formula of various data.

However, some data is missing, resulting in zeroes in the calculated data which the chart uses.

When plotting this data against as a line graph, it's drawing a line down to the axis, which I don't want.

I'd like either a gap in the line, or skip the data point and draw from directly previous to next.

i.e. given this data:

00.0    61.6    39.5    74.6    86.8    72.0    66.5    99.5    85.6    80.6    95.0    122.4
81.0    83.1    88.2    00.0    94.3    60.5    00.0    99.5    95.8    86.2    00.0    111.4
84.1    110.8   78.9    62.0    75.9    102.2   89.9    87.1    81.6    73.5    00.0    116.9

All the 00.0 items mean "no data", so I'd like them ignored (not treated as 0 value).

This is the chart I currently have:

This is how I'd like the chart to come out:

Again, I don't mind if the dotted lines are blank or solid, so long as they don't go down to zero.

The data is dynamic/calculated, so I can't just say =AVERAGE(prev,next) since I don't know where missing data will occur in advance – I need a solution which takes this into account.

Any ideas?