The following snippet will give the average for each month, using the nanmean function. The first column of your_result is the first day of the averaged month. No loops are used but this comes at the cost of more memory. It would be simpler and probably faster to loop through every column of data.
your_data = [randi(42,1,11);[(721000:721000+999)' rand(1000,10)]];
%Getting rid of header
data=your_data(2:end,2:end);%(2:end,2:end);
[m n]=size(data);
fecha=your_data(2:end,1);
header = your_data(1,:);
%Adding up monthly data
%Creating unique index for accumarray function, avoiding looping through
%columns
col=(1:n);
col_mat=repmat(col,m,1);
col_vec=col_mat(:);
fecha_vec=datevec(fecha);
%Reducing year idx
orig_year=fecha_vec(:,1)-min(fecha_vec(:,1))+1;
year_idx = unique(year(fecha));
year_idx = datenum(year_idx,1,1); %idx given as first day of month
idx=[orig_year fecha_vec(:,2)];
month_idx=accumarray(idx,fecha,[],@min);
idx=repmat(idx,n,1);
idx=[idx col_vec];
data=data(:);
%Aggregating data
meses=accumarray(idx,data,[],@nanmean,NaN);
%Rearranging in a three dimensional matrix
meses=reshape(permute(meses,[2 1 3]),length(year_idx)*12,n);
%Recreating and adding headers (column and vector)
month_idx=month_idx';
your_result=[header; [month_idx(:) meses]];
your_result(your_result(:,1) == 0,:) = [];
